Closed Vasectomy describes the ‘testicular end’ of the tube being sealed at the time of the vasectomy.
On the other hand, open Vasectomy leaves the lower end of the tube ‘open.’ Dr Beatty is certainly able to do this for you. In fact, open vasectomy involves one less step than closed vasectomy.
An open vasectomy would fail if the upper tube was only sealed with cautery. If you think about it, an open vasectomy with just a simple seal of the upper end would be inviting the two ends to re-join. The reason that Dr Beatty is able to offer open vasectomy is that he routinely performs fascial interposition on the upper end.
Unless you ask he will perform a closed vasectomy because he believes that the failure rate of closed vasectomy combined with fascial interposition is extremely low, and that the evidence that open vasectomy reduces congestion is very much open to debate. It’s your choice, and he’ll do an open one if you believe this is better for you.