  We study how relative quantum cohomology, defined by Tseng--You and
Fan--Wu--You, varies under birational transformations. For toric complete
intersections with simple normal crossings divisors that contain the loci of
indeterminacy, we prove that their respective relative $I$-functions can be
directly identified. For toric complete intersections with smooth divisors, we
prove that their respective relative $I$-functions are related by analytic
continuation. We also study some connections with extremal transitions and FJRW
theory.
