Combine first 3 ingredients. Dredge steak in flour mixture.
Brown steak, in batches, in hot oil in a large skillet over high heat 1 to 2 minutes on each side. Remove steak from skillet, and place in a lightly greased 13- x 9-inch baking dish.
Sauté sliced onion, chopped bell pepper, and mushrooms in skillet over medium-high heat 5 minutes or until tender. Add pizza and tomato sauces, and simmer 15 minutes; pour over steak.
Bake at 350° for 45 minutes. Uncover and sprinkle with cheese; bake 15 minutes or until cheese melts.