Fundamentally, one of the major reasons Justinian failed to take Italy easily was that Vitiges manages to communicate the amount of forces committed in Italy to Persia.
Very simply, lets assume that by pure misfortune, or betrayal, Vitiges' letters never reach Persia (perhaps a turncoat handling the letters, or the ships carrying the letter are intercepted and the letter is found).
What are the side effects? Does this mean a smooth conquest of Italy (minus the sack of Mediolanium) ? Would this allow the Empire to raise a new Army of Reconquest from Italy - whilst dedicating forces back to fight Persia?