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There is a large number of different ways of constructing Calabi-Yaumanifolds, as well as related non-geometric formulations, relevant in stringcompactifications. Showcasing this diversity, we discuss explicit deformationfamilies of discretely distinct Hirzebruch hypersurfaces in $\mathbb{P}^n\times \mathbb{P}^1$ and identify their toric counterparts in detail. Thisprecise isomorphism is then used to investigate some of their special divisorsof interest, and in particular the secondary deformation family of theirCalabi-Yau subspaces. In particular, most of the above so called Hirzebruchscrolls are non-Fano, and their (regular) Calabi-Yau hypersurfaces areTyurin-degenerate, but admit novel (Laurent) deformations by special rationalsections as well as a sweeping generalization of the transposition constructionof mirror models. This bi-projective embedding also reveals a novel deformationconnection between distinct toric spaces, and so also the various divisors ofinterest including their Calabi-Yau subspaces.

Hirzebruch Surfaces, Tyurin Degenerations and Toric Mirrors: Bridging Generalized Calabi-Yau Constructions