How can I change regions?
I currently live in Canada but I am moving back to Europe in about half a year. Can I take my Canadian purchased Diablo 3 game back to Europe and play it there without any problems?
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Yes, you can play. Please look at this question for further instructions.
And no, not without problems. If you expect your characters to be available on your "european" account then you are out of luck.
You can try to play on the american servers with your original characters, but only with a huge delay. Well, you can try it yourself.