Mac App Store, reuse apps after changing country
For App Store, see this answer for "Do I need to repurchase apps if I moved countries?":


  All the apps you bought in country A are permanently assigned to your AppleID. Once you move to country B and you updated your details (billing address) you:
  
  
  still can use them  
  you cannot re-download them  
  you cannot update them  
  you cannot convert your music to iTunes Plus (but still can listen, obviously)  
  
  
  There are two solutions to this:
  
  
  Switch Store's country and update your billing details each time you want to get your apps up to date (or re-download them). But this is a rather painful process, so a better solution is to...
  Create a new AppleID with the billing details for the country B. Switching between AppleIDs is much easier and quicker than switching Store's country and updating your billing address.
  
  
  Let me quote why it has to be this way:
  
  
    [...] this how iTunes has been designed.
  




For MAS - recover purchased apps on Mac App Store (formatted better and corrected typos):


  Dah•veed
  Re: recover purchased apps on Mac App Store.
  Sep 14, 2013 10:16 AM (in response to Mariokart)  
  
  When you switch regional/country stores your Purchases list does disappear and the MAS will no longer alert you to an update that may be available for an app.
  
  However, all is not lost. But the one caveat is that is an app that you bought in a particular store is not sold in the new store then you cannot update it. Apps that are available from both stores can be updated, it's just that you basically need to hear through the grapevine that there is an update for the app. Then you go through the steps of buying the app and in the final steps the MAS recognizes that you have previously bought the app and downloads it for free. Once you have done this with an app it again appears in your purchases list for the new store and you are alerted to any further updates as before. You have to go through this process with each app.




Also see iOS: Changing the signed-in iTunes Store Apple ID account