Anastomosis procedures are achieved through the use of a system adapted for use with an intraluminally directed anvil apparatus having an anvil pull extending from an anvil. The system has an engager for engaging the anvil pull so that a vessel can be distended by the anvil as the anvil pull is pulled. The system has a cutter for forming an opening in a vessel. The system is adapted for use with a compression plate apparatus used to eversion and holding everted surfaces around the opening together. The system can also be used with an externally positioned anvil apparatus.