Integral Bott--Chern cohomology of Generalized Calabi--Eckmann threefolds

We compute the integral Bott–Chern cohomology of a class of generalized Calabi–Eckmann manifolds of complex dimension $3$. Although these manifolds are mutually non-biholomorphic, we show that their integral Bott–Chern cohomology rings are nevertheless isomorphic. A cohomological distinction is then obtained via a characteristic map in cohomology, connecting singular, Dolbeault, and integral Bott–Chern cohomologies.