Take a look at this link from April 2014 which has a 4. e3 Slav game, note the comment on White's 4th move.
http://en.chessbase.com/post/gashimov-r9-all-rests-on-one-game
I'm guessing the 4. e3 Slav is a variation where black has to be careful not to be lulled into a worse position. Of course, white probably has to be a really good player to extract the most out of it.
I've been playing 1.d4 for two years or so and expanding my repertoire bit by bit, but the semi-Slav has always given me trouble. The anti-Meran requires a surgeon's positional touch while the Bg5 stuff is deeply theoretical incredibly sharp. The only advantage to having such a difficult time finding my feet in this opening complex is that I have played virtually all of the main lines from the white side, and I don't really have a preference.
What I would like from this discussion is not a repertoire recommendation or a line dump but a selection of model games for white that make good study material. I've looked through databases myself and come up with some interesting stuff, but I know there are a lot of 1.d4 players on this website who are more experienced. So let's have it - what are some of your favorite games in the semi-slav?