Which episode of Fullmetal Alchemist Brotherhood had a lot of transitions with a black screen and white text?
I believe you're looking for the Youswell flashback, in episode 38 at around 6:52. This may not be what you're looking for, since it doesn't repeat throughout the episode; however, it's the only one I can really think of.

It starts with a black screen stating １９１４年 (year 1914), followed by ユースウェル (Youswell), followed by various shots of the town and Yoki.



These shots are interlaced with black screens of white text showing the dialog these characters are saying while in the flashback, since Yoki is narrating the scenario.