For income tax purposes, the only deduction will be property taxes (if you don't have a mortgage). The property taxes can only be deducted by the person who legally owns the property AND if that person actually pays the taxes. (So if you put the property in your parent's name but you pay the taxes, no one can deduct them.)
But as indicated by others, the taxes is a small part of the situation, there are a lot of possible complications when dealing with older parents. You should work with an estate planner and tell them what your goal is (avoid probate, etc.) and let the estate planner tell you the best legal way to achieve the goals.
