The present invention is a method of practicing transcatheter valve replacement (TAVR) employing an expandable hollow mesh-like catheter which may be inserted through an aorta to the proximity of a diseased or degenerated aortic valve in a retracted form and then expanded to compress the valve to open it up. Subsequently a new valve will be placed on the collapsed mesh, will be fed through the aorta, and the mesh will be expanded to push the leaflets of the old valve aside. The mesh does not block blood flow, eliminating the need to instigate a rapid heartbeat as required in the prior art procedure employing a balloon rather than the mesh.
