We study the structure of K-theoretic blowup equations–both unity and vanishing. We find the full set of K-theoretic blowup equations for all rank one and many higher rank 5d \(\mathcal {N}=1\) gauge theories. Our strategy is starting from 5d Kaluza-Klein (KK) theories compactified from 6d SCFTs and translating all elliptic blowup equations to K-theoretic ones. Then we reduce the blowup equations by decoupling one at a time the hypermultiplets in various representations. We find the 5d dualities are highly non-trivially reflected in the map among blowup equations. We also study the blowup equations near the 5d SCFT point and find the enhanced global symmetry appears naturally. In particular, all r fields form Weyl orbits of the enhanced flavor group in the lattice of invariant Coulomb parameters. This is a short summary on a joint paper with Lee and Sun [1] for the Proceedings of the Nankai Symposium on Mathematical Dialogues in 2021 August celebrating 110th anniversary of the birth of Prof. S.-S. Chern.