Tolstoy's style seems to favor a good coordinating conjunction – you know, and, but, or and so on. If you look at any extended passage in Anna Karenina, chances are you'll see piles of sentences starting with these conjunctions. This type of sentence structure indicates that whatever comes before the conjunction is both connected to and just as important as what comes after.
The effect this has is to make Tolstoy's long paragraphs like logical accumulations of ideas: piles on piles of sentences that create a total portrait of a character's inner thoughts. By throwing lots of ifs, ands, and buts at us, Tolstoy's style gives us the impression of completeness. Each paragraph is like a perfectly self-contained house, with early sentences providing perfect foundations for later ideas and observations.
Just as Tolstoy's larger plot ideas flow logically from conflict to complication to solution, on the sentence level, his words move from one sentence to the next smoothly and easily, as though nothing in the novel could be phrased any other way.