Minky Momo in Tabidachi no Eki

It is said that train stations are not only an end and a beginning for many, but also are a place for lost and forgotten objects—and for those who are forgotten. On a rain-soaked day, Minky Momo rides the train toward her final destination and ends up conversing with an old man who is trying to reunite with someone very important to him. After discovering he left his passport on the train, Momo embarks to try to find him and consequently runs into both her parallel self, and a young girl who is in need of both of their help. She has ties to the station, and yearns to find a resolution to her troubles...

(Source: Anime-Planet)