Considering that the force of the "then" in Matthew's account is "at that time," rather than "afterwards", there is really no difference between the three accounts. Matthew is locating the beginning of persecution at the time of the things that had been mentioned before. Mark seems to be addressing the persecution as if it was occurring within the stream of events mentioned previously (false Christs, wars, earthquakes, famines, etc). Luke places the persecution as occuring before (at least) the terror and signs in the heavens.
Persecution of those bearing the name of Christ, according to the Olivet Discourse, will start in the midst of the signs stated in the first third of the discourse, and will proceed until the end of the age. It will proceed to the end because: 1) disciples cannot be hated by all nations until all nations have been confronted, at least to some degree, by the gospel; and 2) we are told that those who endure (persecution, et al) to the end will be saved. According to Jesus, being hated is something all true Christians ought to anticipate through all time, everywhere.