Was Anne’s relationship with her sister Mary built on rivalry as it is clearly stated in books about their lives? Thanks a heap!
Unfortunately, we just don't know, but there is no reason to believe that it was one of rivalry like that of books like "The Other Boleyn Girl". We know that Mary did attend on Anne (she is listed in 1533 as one of the women given a New Year's gift from the King) and she also attended on Anne at her coronation. She then crops up again in September 1534 when she arrives at court pregnant and announces that she has secretly married William Stafford. Anne is understandably furious with her for marrying without her family's consent and banishes her from court, but this does not mean that there were always problems between the two women.
We don't know for sure whether Mary ever came back to court although the Bishop of Faenza has her attending on Anne in January 1536 when Anne miscarries. See http://www.theanneboleynfiles.com/mary-boleyn-part-three-1526-1543/6143/ for more information.