  We introduce a new technique for approaching birationality questions that
arise in the mirror symmetry of complete intersections in toric varieties. As
an application we answer affirmatively and conclusively the question of
Batyrev-Nill (2008) about the birationality of Calabi-Yau families associated
to multiple mirror nef-partitions. This completes the progress in this
direction made by Li's breakthrough (2016). In the process, we obtain results
in the theory of Borisov's nef-partitions (1993) and provide new insight on the
geometric content of the multiple mirror phenomenon.
