If ASL time - travels, Luffy's relationship with his brothers would be strengthened in new ways. They would have to rely on each other more as they face the unknowns of the past. For example, Ace might see a younger Luffy and be even more protective.
If Sakura travels back in time, her relationship with Sasuke would be very different. She could meet a younger Sasuke who hasn't been through all the traumas yet. She might be able to form a closer bond with him from the start and change his path. With Naruto, she could become a mentor - like figure if she travels to a time when he is younger, guiding him in a different way than in the original timeline.
His relationships with his guild members would also change. He could prevent some of their deaths or mistakes. For example, he might be able to stop Klein from getting separated from the group at the start of SAO. This would lead to a different dynamic within the guild, with more camaraderie and a sense of unity.
In a time - travel scenario, Anakin's relationship with his mother could be greatly altered. He could go back in time and save her from the Tusken Raiders. This would change his whole outlook on life and his path towards the dark side. Regarding his relationship with Palpatine, he would be aware of Palpatine's true nature from the start. So, he could either avoid Palpatine completely or try to expose him earlier. His relationship with other Jedi, like Ahsoka, could also be different. He could be a better teacher and mentor to her, as he has the experience of his future mistakes.
If Kakashi travels back in time, his relationship with his father would be completely different. Instead of the strained relationship due to his father's perceived failure, he could support his father and build a strong bond. With his students, if he travels to the future and then back, he might have a new perspective on how to train them. He could be more lenient or more strict depending on what he saw in the future of their development.
Baymax would need to adapt to different time periods. His knowledge base might be limited in some historical times. He could learn new things and update his database, which could change his personality a bit. Maybe he'd start to have a more historical perspective in his responses.
His relationship with Obi - Wan would also change. If Anakin travels to a time when he was just a young Padawan again, Obi - Wan might see a different side of him. Anakin could use his future knowledge to become a better student, and Obi - Wan would be proud of him. Or, if Anakin travels to a time before he met Obi - Wan, he could approach their relationship from a new perspective when they do eventually meet.
Well, his relationship with Vegeta would be interesting. If Goku went back in time and showed Vegeta the SSJ God form too early, Vegeta might become more competitive or even jealous earlier. He might push himself even harder to catch up, which could lead to more intense rivalries and also more joint training sessions between them.
If Walter goes back in time, his relationship with Skyler would be completely different. Instead of lying to her about his meth - making activities, he would be honest and they could build a more trusting relationship. They might even have a normal family life without all the secrecy and danger.
The relationship between the Black Knights and Lelouch would also change. If Lelouch goes back in time and is more strategic from the beginning, the Black Knights might be more unified and loyal to him. They would see his long - term vision more clearly and be more willing to follow his every command, which could lead to a more powerful and efficient resistance against Britannia.
GoGo might become more patient. In a time - travel situation, she'd have to deal with the differences in technology and culture of the past. This would force her to slow down and adapt, which could lead to a change in her typically impatient personality. She might start to appreciate the process more rather than just focusing on the end result.