An anastomosis is performed using a flexible mounting structure mounted on the
outside of at least one vessel. Fasteners extend through the vessel and are bent
towards the incision to attach the flexible mounting structure to the vessel in
a manner that controls the edge of the vessel adjacent to the incision. The mounting
structures are oriented on each vessel so fasteners on one mounting structure interdigitate
with fasteners on the other mounting structure at the location of contact between
the vessels when the two vessels are brought together. This creates two complementary
sinusoidal-shaped vessel edges with peaks of one edge being accommodated in the
valleys of the other edge. The peak-to-valley orientation forms a sinusoidal-shaped
joint which is leak free. The fasteners are spaced so proper pressure is applied
to the tissue to promote healing without leaking. Furthermore, the fasteners are
sized and shaped to properly engage the tissue and bend in a desired manner. Methods
and tools for carrying out the anastomosis according to the invention are also
disclosed. Methods for forming the fastener and the tines having the proper characteristics
are disclosed. An absorbable ring-shaped stent is also disclosed.