In a medium bowl, combine the flour, 1 t. salt, and 1/4 t. pepper; coat the steak with the mixture.
In a large skillet, heat 4 T. of the oil over medium-high heat; add the steak and cook for 6-8 minutes, turning halfway through. (If your skillet is not large enough to cook all the steak at once, cook it in two batches, adding more oil if needed.) Remove the steak from the skillet and set aside.
In the same skillet, heat the remaining 2 T. of oil over medium-high heat and saute the celery and onion for about 5 minutes or until tender. Add the carrot slices, spaghetti sauce, and the remaining salt and pepper; mix well. Add the steak to the mixture, reduce the heat to low, and simmer, uncovered, for 10 minutes or until warmed through.