The past, present, and future do not exist as separate states.
Imagine a vast array of all possible states of matter in the universe. Imagine reality has a finite spacial resolution. With a series of numbers, or even a single very large number, you could provide a unique identifier for every possible arrangement of matter in the universe. The positions of every star and galaxy. The detailed interactions of every quark. Imagine a list or array that would have a number of entries equal to some indecent multiple of "ten to the ten to the ten...." Imagine all these possible states, every possible configuration the matter of the universe could occupy.
Then realize...All of these possible states exist at once. They are all as real as any other. There is no preferred state. They all exist in some vast "10 to the ten to the ten" dimensional spacetime. What we perceive as the flow of time is simply us moving from one of these states to another. But our consciousness cannot move arbitrarily between states. There are elaborate rules on which states you will be able to observe dependent upon the states you previously observed. We call these rules the laws of physics.
So when you travel through time, you are simply altering your path on this vast multiverse of possible realities. There is no "real" reality. They are all real. Every possible configuration of the matter and energies of the universe physically exist concurrently.
There are no timelines to split or erase, because there are no timelines. There are just conscious minds moving through a near-infinite array of possible "nows." And all of the nows exist simultaneously. There is no real one. From the perspective of a "time traveler," it will seem like they changed "the future." But the truth is the very idea of a past, present, and future as distinct entities is madness. We're just consciousness drifting through the continuum, from one of the near-infinite nows to another.