On the subject of stop baths versus water, the following information is taken from the Kodak Black and White Darkroom Dataguide, p14, first paragraph of the section headed Stop Bath:
The primary function of an acid rinse or stop bath is to stop development. It also serves other useful purposes in processing film. An acid stop bath removes the calcium scum that forms on the surface of the film during development, and it prevents excessive swelling of the gelatin coating. By delivering the films into the fixer in an acid condition, the stop bath not only preserves the acidity and the hardening properties of the fixing solution, but also prevents the formation of alum scum and sludge.