I've worked a bit in Poland and UK (before Brexit) and all i had to do was to take a plane and fly to the target city. I do not remember having any particular difficulties, if anything finding a place to live was the hardest thing but that is an issue with moving in general (including within the country), not moving across EU.

I'm not into traveling but i'm pretty sure i can grab a plane/train/bus/whatever and go any EU city i feel like.

Living in a place is quite a bit different to travelling there.

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