The tissue approximating structures for the anastomosis devices of the invention preferably include two sets of approximating structures or tines spaced from each other along the length of a catheter body that can be extended and retracted from the catheter body. Each of the sets of tissue approximating structures is preferably sequentially deployable in such a way that the surgeon can activate a first set of tines to engage a first tissue structure, verify that an adjacent second tissue structure is properly positioned relative to the first tissue structure, then activate a second set of tines to engage that adjacent second tissue structure. Each of the sets of tines is preferably controlled by a single actuation mechanism that is attached to the anastomosis device and is positioned outside the patient's body.