Uma etapa de uma viagem longa pode ser chamada "a leg" em inglês. Veja: http://www.merriam-webster.com/dictionary/leg (6b).
Not just texas; and it's not that informal. Airlines and travel agencies use it all the time.
Merriam Webster gives:
6 a : the course and distance sailed by a boat on a single tack b : a portion of a trip : stage c : one section of a relay race d : one of several events or games necessary to be won to decide a competition won the first two legs of horse racing's Triple Crown
"phase" = «fase», while «etapa» = "stage"
P.S. Also, "ends" would be a better option here. "stops" almost always requires a direct object: "I stop the bird from crossing the street," "Superman stops the villain from executing his dastardly plans," etc. "ends" does not need a direct object and is better suited for things that reach a closing point without mention of any external forces.