Your home of record doesn't change no matter where you live. You can buy homes at every duty station you get and you are still a resident of your home state. (That only changes if you start renting them out.)
Each state has different rules on how they deal with active duty personnel who are stationed elsewhere. I posted California's and North Carolina's below but if you're getting transferred it's a good idea to look up the rules for wherever you land.
Here are California's rules.
Here are North Carolina's rules.
You can also change your SLR with the military if you choose.
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