In general, there are two schools of thought when it comes to luminaries as they may exist on the "cusp". For purposes of this entry I'll go along with the pedestrian flow and use the Sun sign in discussing them, along with my revelation about which seems to hold more true in practice.
I assume everyone landing on this article gets the concept of a cusp. It's not an astrological term after all but a bona-fide open entity in the world of linguistics and literature. If I Google the definition of "cusp", which I just did, the top result explains it as the period of transition between two states.
It's just so associated with astrology because, well, damn -- in astrology there are so many changes between "states". Planets cross the borders of houses and signs, and even aspects can have cusps.
People who talk and learn casually about astrology who are cusp-born typically know it. They are honed to learn this over time when, using their birth date, they come to realize that every astrological profile they set down to absorb differs on whether they are "in" one sign or the next.
It would certainly breed a sort of skepticism about astrology if nobody could tell you which g--damned sign you actually were. Though perhaps you should be tortured if you're taking anything from knowing your "Sun sign" anyway -- though I digress.
Then, such a person meets a schlub like me in a bar, someone trying in the most unimaginative and outdated of ways to procreate through drinking among random strangers with "What's your sign" pickup lines to anyone dumb enough to seat themselves partnerless in my proximity (we'll have to assume the person is a woman, but then, have I ever really disclosed my sexuality? This is 2020 people, get with it!), which then leads to a discussion of astrology way beyond what that person may have been expecting -- or wanted.
Assuming I don't get the turn-and-shoulder block at this point, or my prospect doesn't manage to send the secret "bartender I gotta creepo here'" signal, I can get down to the nitty gritty. In a rare moon, a fellow bar patron in this context is genuinely interested.
In most cases, I explain, you don't have to tell people you are born on the cusp of anything. You actually are one sign or the other, if we even agree the Sun sign means jack-widdly anyway. But yes, you have to determine what that "one thing or another" actually is by having a bona-fide birth chart done, based on the best birth time you have available.
The Two Schools
As I mentioned, there are two schools of thought among astrologers once the question is sorted out by a real chart calculation.
The first school says to you something like, as the Sun moves toward one sign and wanes from the other, it transfers the energy gradually, so you in fact could be factored by both signs while this occurs.
I like that idea the most because when you step back from the entirety of the zodiac, consider that a "sign" or a "house" is actually just a collection of degrees.
Any degree of a point on the chart should be defined by its distinction from the 359 other degrees around it. So, Aries is only Aries because it subtracts and adds the influence of the 11 other signs such that, in that circle, it has its own expressive energy. In short, Aries is Aries because it is Taurus, but since Taurus lacks some attribute of Aries while adding others, it can't really be Aries. Moving on, Aries is Gemini, except Gemini can't really be Aries because Gemini lacks, or adds, some attribute of Aries. And so on.
If the energy of a degree on the zodiac wheel exists because it is the sum of all energy it couldn't be among the other 359 degrees, which themselves exist in influence for the same reason, it only makes sense that the weight of a sign's influence evenly and poetically passes off in these incremental changes as it moves through the wheel. Hence, an Aries born on the cusp of Taurus might well appreciate that they have the weakest Aries qualities along with the strengthening Taurus ones, because that makes the most sense.
But, then there is the other school of thought -- and keep in mind that I have not yet revealed my own experience or preference in this question.
The other school looks at the beginning of each sign as a "reset" of the former influence. You simply cannot be an Aries if your Sun is at 1 degree Taurus. Or even zero dot half a degree. Once the Sun leaves the previous sign, the influences of that sign evaporate. You are left a weak child of the new sign's influences which in a way have not yet coalesced into the attributes and personality traits so commonly associated with it.
I hate that vision of how it works because it tosses out the symmetrical uniform beauty of zodiac degrees all existing as the total sum of what all the other degrees have and don't have. And, dammit, I am a systems person. Signs that mysteriously drop their influence at fixed points on the zodiac wheel then "magically" acquire a new one, is just too much a process to wrap my head around.
But (sigh) as much as I cringe to say it, over time, I've come to find more in truth with the latter school of thinking than the former.
The Reality is a Scream
Of course I have my usual twist on the why, which is that while I don't so much find a weak influence of the sign being transitioned into, I do consistently find that a planetary or astrological sign is a sign no more certainly that sign than when it is in the final degrees of it.
Absolutely, hands down, no foolin'.
A Leo personality is no greater a Leo personality than when the Sun (or, let's get real, Moon) is in the final degrees of Leo. A Sagittarian is no more expressive as a Sagittarian than when it is in the final degrees of Sagittarius.
I suppose if you wanted to look at this way, the early degrees of a sign seem to be tepid expressions of it. Then, as the degrees gain strength in that 30-mark window, they mature and take on more visible and absolute traits long associated with that sign, until finally they reach the end -- the 28/29 degree mark -- where they are fully developed and, morbidly facing their demise as they prepare to transition into the next sign, begin to scream loudest. When you think about it, ain't that how people behave?
If we wanted to "prove" astrology and needed a dynamic to rely on, we could start with this concept, because in my experience, it is that reliable. But assuming my experience is correct, why do cusp people believe they are blended personalities?
We're all just speculating here but I'll offer up that at the most fundamental level, for the very reasons I banged out above, it's just easier to believe that blending is a real thing. I sure as hell wanted to believe that's how things work.
As well, there is confirmation bias at an astrological level. You see, the location of the Sun at birth effectively places the location of Mercury and Venus. These planets will either exist in the sign just before, in the same, or just after, whatever the Sun is in. These two planets are relatively speaking very personal (though, nowhere near as much as the Moon or rising sign), and go a long way to developing a certain personality. A good body of people, let's just say half, will have their Mercury or Venus in the preceding sign (Aries if it is someone born on the Aries/Taurus cusp, but on fine analysis of the chart shows they are Taurus), so will have very key Aries qualities to their personalities. Someone with the Sun at 29 degrees of Aries but with a Taurus Mercury could be forgiven for thinking themselves genuinely blended with Taurus stuff due to the cusp.
And then of course, there is the rest of the chart. Most births occur in the morning, just after sunrise in fact. This means people of a given Sun sign will have rising signs that are next in line of it. So, yes, for sure, a Cancer Sun sign person is very likely to have a Leo rising sign (statistically speaking only) which would lead anyone born on the end cusp of Cancer to logically conclude they are simply blending their Cancer farts with Leo farts. And as well of course, there are other more random placements such as the Moon or other aspects, that could similarly fuel the belief.
Leave your questions as comments for a response here or on the YouTube channel (which I'll beg you to subscribe to).