How to get number of begin transactions in PostgreSQL?
A_horse_with_no_name's comment had me curious, and it seems like PostgreSQL doesn't use transactions in the same way that you're used to in Microsoft SQL Server. Rather they use Save Points. This StackOverflow answer gives a little context about Save Points and how to track them (see the comments on the answer for additional details).
There typically can only be one transaction open at a time, but you can achieve nested transactions utilizing save points.