It depends on a lot of factors. If you being transferred because of your employment, it's one thing. If you considering moving just to make it more difficult for the other parent to be with the child, it's a vastly different thing.
The courts in all States do not take kindly to vindictive actions on the part of any party in a custody dispute. If they think you are deliberately trying to deprive the other parent of his/her visitation rights, it will not go well for you. If you have custody, you could lose it.
Consult with your attorney on any action you are contemplating.
Here's what you have to remember: it is the right of the child to have two parents. It is the right of each parent to have a close, personal relationship with the child.
You might ask yourself why you are calling it a custody battle? The health and well-being of the child you and your spouse brought into the world is supreme.
Joe(find a way. good luck)Nation