Yes, this is chapter 7 of [Fosco Loregian's thesis][1], linked from his webpage. The paper Simone Virili linked to is one of 3 papers making up the thesis. Specifically, Section 7.2.1 discusses the topology, after Bridgeland, and proves the comparison you asked for. The setting is a slight generalization of that of Bridgeland's original papers, as Loregian makes clear.


  [1]: http://www.math.muni.cz/~loregianf/stuff/main.pdf