His stories are generally very brief. Instead of filling them with details and symbols, he usually just gives us an "impression" of something. He's impressionistic. This is not to say that he never uses symbols. Of course he does, but not like Lawrence, for example. Chekhov will give us an "impression" of the character or an "impression" of the landscape or an "impression" of the theme. This is not to detract from Chekhov's skills, either. Not many storytellers are able to capture so much in so little. Often, rather than following a linear plot, Chekhov just gives us an impression. His use of mood, character, scenery, etc. are all very impressionistic, and all to the good, but sometimes it takes a little longer to work everything out.
I can't agree with the connection between Peter and Ivan, though. I think the connection is just that - connections. I think, through the retelling of the story of Peter to Vasilisa and her daughter, Ivan comes to realize that all of life, from the very beginning is interconnected. He comes to realized the interconnectedness in life.
Ivan first mentions that the same cold wind blew during the the time of Rurik, Ivan the Terrible and Peter the Great (Russian Czars) and then he believe Vasilisa and her daughter, because of their tears, must identify in some way with the story of the apostle Peter. And I think they do. I don't think it's from darkness to light, but rather a realization that all of life is interconnected and we are all a part of one undivided whole. The past is connected to the present and the present will be connected to the future.
Perhaps I'm living up to my "Russianness" after all!

I don't really know.