Mechanics of the Inuyasha love triangle? A large portion of the InuYasha manga and anime series deals with the emotional issues surrounding the primary love triangle of 


   Inuyasha, Kagome, and Kikyo, particularly from Kagome's point of view. However, it is revealed that Kagome is, in fact, a reincarnation of Kikyo, so they actually share the same soul, albeit from different time periods!


If that's the case, then this appears to remove all of the tension and underlying conflict, in effect Inuyasha is in love with


   the same person (in two forms, one of which is even a vengeful spirit of the dead who wants to move on the afterlife)!


How exactly was this love triangle supposed to work, narratively? While I can't speak for the mangaka's inner thoughts, perhaps there are cultural nuances or tropes that I'm not aware of at work here?
The mechanics work like this:

Inuyasha is in love with Kikyo. She is the first human since his mother that treats him well. Despite Kikyo killing him and sealing him to the great tree, he still loves her.

Kagome falls in love with Inuyasha at first sight, but he doesn't like her at all. When he firsts revives from death, he thinks it is Kikyo, but once he figures out she is someone different, he doesn't care for her. 

Due to framing plot reasons, Kagome and Inuyasha have to work together to save the world. Inuyasha slowly starts to warm up to Kagome over time, as she overcomes the dead Kikyo's shadow. Then Kikyo gets resurrected (as a walking dead corpse). This causes Inuyasha's cooling love for Kikyo to flame strongly again, and causing him to be torn between his first love (Kikyo) and has new growing love (Kagome). However, his loyalties are first to Kikyo, so Kagome always loses out when he must choose between them.

Inuyasha's first loyalty is what prevents Kagome from being able to "seal the deal" with him, and is a hurdle she can never overcome as long as the animated dead Kikyo is around. No matter how close Kagome and Inuyasha become over time (in the main series), he will desert Kagome to run off and save Kikyo if he thinks Kikyo is in danger.