While clunky this is how the Pokemon anime could've worked. Each season or region could've been self contained. I mean I can't be the only one wanting a new main character to replace Ash. Also a review of Madoka Magica or Magikano could be fun. That's not a request just a suggestion.
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Dude, what did you say?
You can store Pokemon caught in the E-Shop game in Pokemon Bank.
You could catch a Mankey in Route 22 in Pokemon Yellow. A nice reference to the Anime, where Ash caught a Mankey.