Let X be a Calabi–Yau manifold that admits a Tyurin degeneration to a union of two quasi-Fano varieties X1 and X2 intersecting along a smooth anticanonical divisor D. The “DHT mirror symmetry conjecture” implies that the Landau–Ginzburg mirrors of (X1,D) and (X2,D) can be glued to obtain the mirror of X. Initial motivation came from considering the bounded derived categories of X, X1, and X2 and symplectomorphisms on the Landau-Ginzburg models mirror to (X1,D) and (X2,D). In this talk, flipping the roles of the two categories, I will explain how periods on the Landau-Ginzburg mirrors of (X1,D) and (X2,D) are related to periods on the mirror of X. The relation among periods relates different Gromov-Witten invariants via their respective mirror maps. This is joint work with Fenglong You and Jordan Kostiuk.