Can a different state have jurisdiction on an existing case?

I divorced in the US, Arizona, and had a joint custody order entered for the children. When I relocated overseas for work, the AZ court deferred jurisdiction to Italy, I have lived in Italy for 4 and a half years with the kids. The local financial crisis is seriously making me consider moving back to the US, it's been just too difficult to find work. My question is, once the original AZ court deferred jurisdiction to another country, and I move from that country back to the US, would jurisdiction go back to the AZ court automatically, or does jurisdiction once relinquished go to whatever other state I move to, wherever I find a job, and establish residency? In other words, am I free to move anywhere in the US once I make the decision to go, or do I have to move back to the same state I left when I moved to Italy? Please let me know. Thank you.