You actually need to know the equivalent of Service_Start and Service_Destroy, which you use to open and close the DB, but this isn't strictly DB-related.
Open the DB by calling a method of your DBCalls (modDB) from within B4XPage_Created of the B4XMainPage. The actual entry point is the Initialize Sub of B4XMainPage, so this would be the most appropriate place.
First of all, in my opinion (!) closing a SQLite DB isn't essential, as it doesn't is / have a server; it's important to close always all the ResultSets.
Service_Destroy. The equivalent "should" be the B4XPage_CloseRequest Sub of the B4XMainPage, but that's not certain, as your project might want to close this page without closing the project.
I'm about to write something that could be not correct (confirmation from Erel would be needed) ...