The question of personal identity is a tricky one and philosophers have argued about it for a long time, considering the Ship of Theseus and other analogies in that context.
One way to frame it is to think about past and future selves. Putting it this way is biased in the sense that it implies that these are not the same as the current self, thereby foregoing the conclusion. But it allows to ask questions like
How strongly do you identify with your past self?
How well do you treat your future self?
which can be quite helpful mental tools.
The secion on exactly this subject was what I found most intersting in the chat between Simone Collins and Spencer Greenberg that I listened to the other day. They talk about much more than this and at times it is quite funny (the good kind of funny).
Plus, they mention FutureMe, a site for writing letters to one's future self - what a wonderful idea!