An everter and threadthrough system useful for attaching a graft vessel to a anastomosis device which can be used to attach a graft vessel to a target vessel without the use of conventional sutures. The threadthrough system engages an end of the graft vessel and pulls the graft vessel through a deployment tool until a portion of the graft vessel extends beyond a distal end of the anastomosis device mounted on the deployment tool. The everter includes a spreading mechanism which expands the end of the graft vessel and folds the expanded end over the anastomosis device. In the case where the anastomosis device includes barbs, the everter can effect penetration of the graft vessel by the barbs. Once the graft vessel is everted over the anastomosis device, the deployment tool can be used to attach the graft vessel to a target vessel.