Proposition for step, stage, and phase

During seems to work with all of them; At doesn't work well with phase.  A phase seems to me to be longer or more complex than a stage, and certainly more so than a step, which is conceptually even shorter/simpler.  However, the idea conveyed by all three words is essentially the same; just use one consistently when describing a process.  I would guess that certain fields or processes habitually prefer one of the three over the others, so you may want to examine similar writings before making your word choice.