Each ascension is presented as a different individual, with Astarte as her first ascension, Space Ishtar as her second ascension (nicknamed Ishtarin), and Ishtar Astarte as her third ascension.
Astarte and Ishtarin were originally fragments of the primordial goddess Astarte Origin, being split into good and evil halves. Ishtarin was raised by Professor Tokiomi and started work as a bounty hunter alongside Calamity Jane after his death, while Astarte was raised by Munenori to be the emotionless leader of the Space Shinkageryuu. While Ishtarin was initially assumed to be the good half and Astarte the evil half, it's revealed in one of Tokiomi's recordings that the opposite is true. This revelation is what allows them to synchronize into Ishtar Astarte.
Bel Maana is summoned when using their Noble PhantasmEdin Shugurra Quasar, manifesting the massive goddess shrine the size of a galaxy (or rather, a galaxy that takes the form of a goddess).
