My son and I are moving from California to Arizona. His mother just moved from Colorado to Oregon. I want to get the jurisdiction moved to Arizona where him and I are. Do I have to be there for a certain amount of time first and do I have to motion with Colorado court to move it or Arizona?
We have joint custody and he is with me through the school year per the court order. I want to change the custody to full custody on my side since he is with me 9 months of the year. Also she gets to claim him on taxes every other year does not have to pay any child support and I have to pay his tickets to travel back and forth all the time.

I would assume "joint" custody is what you have now, and with you sharing 9 months and 3 months, I don't see how and why you want it changed.

The every other year on taxes is fairly normal and standard, even with "full custody"

Paying for his travel back and forth, what has changed from the original motion and ruling that requires it to be changed other than you not wanting to pay it.

I asked her for help while I am moving. I needed him to stay with her because it is to hard to try to move keep him in school and take care of him. She said he could not come and stay with her. So if she doesn't want to take any responsibility I will go after child support and all the stuff she gets is because I volunteered that in the beginning. And she feels she doesn't have to do anything.

Here are rules for AZ to assume jurisdiction

Residency Requirements for Child Custody in Arizona | eHow.com

Since both parents have moved from the original jurisdiction then it can be moved to where the child now resides after establishing residency.

There are two types of custody, legal and physical. I doubt if you will get full of either type. I don't see any reason to change the current situation. As for claiming on taxes and paying for airfare, that's what you agreed to in the divorce. Unless there is a significant change in circumstances a court will be unlikely to change it.