An extravascular anastomosis device for facilitating side-to-side arteriovenous fistula creation and maintenance of patency thereof is presented. The device comprises two device halves each containing an anastomosis window which is in fluid connection with an interior space of the device. Further, the device comprises a pair of vessel capture spaces in which portions of the vessels to be joined are captured. The invention also has an embodiment wherein a method of joining a vein and an artery in order to create a fistula is presented.