If you are talking about an investment property, it is possible to "swap" investment properties and save on capital gains tax, but it's difficult to do because of the problem of equal value. One option would be to have both properties independently appraised, and the lesser valued property owner would have to pay the difference in cash to the owner of the higher paid property.
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