title: Re-associate another IP to a running instance?
body: <p>I have a complicated use case for this , <br>
  But for short , while an instance is running, can I switch the elastic IP to another one ? and what will happen in this time interval (between de-associating , and re-associating [might be 10-30 minutes] ) .. Won't it be able to communicate over the internet ?  </p>
  
  <p><b>EDIT:</b>
  Great answers so far, but this answers the second part of the question, the main one is , how to change the IP while it is running?</p>