.. you cannot move pool to the vampire you replaced for an Anarch Convert (after he has entered the ready region) in the same influence phase. This applies to using effects like Powerbase: Montreal or Arcane Library, which can only be used during your influence phase. The reason for that is, that the influence phase actually consists of two sub-phases, the main phase where transfers are used for moving blood from/to the vampires and effects like cards mentioned above are used to put blood on the vampires. In the end phase, the vampires with enough blood (greater or equal to their capacity) are moved to the ready region. And as the name suggests, this ends the influence phase.
If you're a nitpicker, you can very often observe players in their influence phase to move blood to one vampire, flip him over and then move blood to a second vampire. From a technical point of view, this is a misplay. After the first vampire has been moved to the ready region, the influence phase already has ended. So consider yourself warned (e.g. when you're in the final of a Continental Championship)!