Apple has just added the Showtime Anytime channel to Apple TV, following its reintroduction of the iTunes Festival channel. The new channel is basically Showtime’s version of HBO Go — it’s been available on the App Store for some time. Showtime Anytime has on-demand content and live streams of Showtime East and Showtime West for authenticated TV subscribers. Some free full episodes of Showtime shows are even available without cable or…