Some ideas are:
- You branch off into another timeline and your actions make no difference to the previous timeline
- You’ve already taken said actions but just didn’t know about it so nothing changes
- Actions taken can have an effect (so you could suddenly erase yourself if you killed your parents)
- Only “nexus” or fixed events really matter, the timeline will sort itself out for minor changes
- something else entirely
Stories involving 2 are often the most fun, as well as 4 if they aren’t lazy with the timeline corrections
1 feels the simplest and I would prefer it. With 3, unless the technology is limited to a few people, it’s going to get messy