Boku no Chikyuu wo Mamotte
English name: Please Save My Earth
Genres: Drama, Sci-Fi
Type: OVA, Episodes: 6
Aired: Dec 17, 1993 to Sep 23, 1994
Studio: Production I.G
Source: Manga
Rating: PG-13 - Teens 13 or older
Synopsis:
Alice Sakaguchi once dreamt that she is another person living on the moon. The dream is so strange and so real that Alice can't stop thinking about it. She finds out that some of her classmates are having the same kind of dream. They soon discover that they had been seeing flashes of their past lives as a team of scientists on the moon. Alice and her friends then decide to find the other members and piece together what took place back then. Complications arise when they realize that everything that happened in their previous existence continue to haunt and affect their present lives. 

(Source: ANN)