Mystery vine, again

I posted some pics earlier, and got guesses including greenbriar and clematis. It’s blooming now, and the blooms look like classic clematis (also, no thorns on the stems, which in researching I see is a characteristic of greenbriar). I’d be fine with that, except I don’t know what pruning type it is (I saw on some site that there’s three) so until I find out what I have I’m not going to know how to properly prune it.
(Update!!! Successfully id’d as clematis viticella by !!! Thanks and thanks to everyone else!)

Here goes:

Overall view:

Flower closeup:

Leaf closeup (the untoothed ones; the toothed are from a nearby virginia creeper):

Extreme flower closeup:

Thanks all!