That's interesting. I mean, an altered timeline becoming the "correct" one. In every movie (not talking now about BTTF, but in general), who says that the first timeline we see is always the correct one, or in other words, the first one?
I've always thought that Terminator had the same thing going. John Connor became a major threat to Skynet, so it sent Arnold back to destroy him. (Trying to do what should NOT be able to succeed). When Arnold arrived and started killing Sarah Connors, I bet one of the earlier ones was the CORRECT one – remember that Skynet had no clue who Sarah was, so Arnold was being methodical.
Then he locates ‘our’ Sarah Connor. But this Sarah - in her own words - is “not the mother of the future. I can't even balance my checkbook!"
If Kyle had not saved her, and put terror of the machines into her, there would have been no John Connor, or if she ever did have a son he wouldn't likely be ready to lead a war against the machines.
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Timeline 1 - One of the Sarah's that were listed earlier in the phonebook had a son named John (John1) who would lead the rebellion. Daddy was a survivalist type. Skynet gets the idea to kill John1 before he is born, and the Resistance sends Bob back to stop him, creating timeline 2.
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Timeline 2 - Arnold and Bob arrive in the past, and Bob succeeds, but is unable to save the earlier Sarahs. He survives the pipe-bomb explosion of the terminator. The police spend a lot of time with him, trying to find the cop-killer. Sarah stays in the hospital until Bob dies of his injuries, then heads out, eventually stopping for gas, but does not get her picture taken because the kid had no more film for his camera, so she has no picture for Bob to see in the future. Sarah eventually has a son, and names him John (John2). As it happens his father is the same man from timeline 1 who fathered John1 (this guy REALLY had a thing for women named Sarah.) So John2 fights the machines and Skynet sends Arnold back. But John2 never met Bob, but he does know a very skilled soldier named Kyle and sends him, creating timeline 3.
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Timeline 3 - Arnold and Kyle arrive, and Kyle tries to save the earlier Sarahs, but like Bob, he is unable to. Kyle can only hope that the remaining Sarah is the correct one. The other major difference is that Sarah becomes pregnant by Kyle, and that Sarah gets to the gas station a day earlier since Kyle died in the factory. The kid still has film in his camera, and takes a picture of Sarah and her dog. This change creates timeline 4.
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Timeline 4 is the movie "Terminator" as we see it. Kyle makes no attempt to save the earlier Sarahs because he knows they are not the correct one, since he has a picture of Sarah, and loves her already.
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In each of these timelines, where useful pieces of the terminator are left behind to be found by CyberDyne employees, Skynet is altered and improved, changing from a 'neural net' CPU to an AI program running on the distributed computing system we call 'the internet'. The neural net CPUs still are used in the terminators, but they are improved versions. It also has even more advanced tech available, allowing more advanced terminators to be sent back in later attempts to kill John Connor - the T1000 and the TX.