A method of creating a native vessel bypass percutaneously includes steps of selecting a target procedural site adjacent to a paired artery and vein, usually near an occlusion or blockage disposed in the artery and advancing a catheter through the vein with its distal tip extending through the vessel walls into the adjacent artery. An anastomosis is formed by applying heat to tissue forming the vessel walls which is captured between surfaces on a proximal base and the distal tip of the catheter. The venous valves are disabled to permit retrograde venous flow of arterial blood, in order to bypass the arterial occlusion.