An attorney would be able to take care of the paperwork and guide you through the transaction.
I would recommend selling your current home and finding the home of your choice in area you are moving too.
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But this is very complex and you'd be much smarter to sell your house and buy another one. If you have a mortgage, and the property is your personal residence, swapping is likely not an option and there is no tax advantage to doing it that way.
My strong recommendation: sell your house and buy another one. Less stress, less complexity, and any real estate agent can help you.
With the swap idea, you'd need to involve a real estate attorney.
Ann Griffin, Realtor
Coldwell Banker Trails & Paths
Swapping isn't unheard of, and no the two properties do not have to be of equal value. each of you has to agree to a sales price or valuation and then the owner with the lesser valued property would simply have to make up the difference in cash.
In each state you'd want a real estate attorney to handle the paperwork to make sure that each "Buyer" got title free and clear.
While I've heard of this, I've actually never met anyone who was involved in such a transaction though I would guess you could Google "Houseswapping"and you'll probably find some sites that are set up from this.