Phaseshifting is Angel's Siren power. As Lilith can Phasewalk to navigate the battlefield safely, and Maya can Phaselock an opponent to immobilize them, Angel can Phaseshift. This allows her to almost instantly and effortlessly hack any technology in a network she is connected to, either directly or indirectly. Throughout the Borderlands 2 storyline, Angel uses her power to interface with Hyperion technology, or electronics that are connected to Hyperion equipment. Each time Angel Phaseshifts, she announces "executing phase shift."
When destroying the units that constantly supply Angel with Eridium, Angel will conjure boxes of ammunition for the player, by means that appears similar to the Digi-struct module used by Catch-A-Ride stations. It is possible that this is another aspect of Phaseshifting.