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Let $X$ be a compact complex manifold, and let $\pi: \mathcal{X} \rightarrowB$ be a small deformation of $X$, the dimensions of the Bott-Chern cohomologygroups $H_{\rm BC}^{p,q}(X(t))$ and Aeppli cohomology groups $H_{\rmA}^{p,q}(X(t))$ may vary under this deformation. In this paper, we will studythe deformation obstructions of a $(p,q)$ class in the central fiber $X$. Inparticular, we obtain an explicit formula for the obstructions and apply thisformula to the study of small deformations of the Iwasawa manifold.

The jumping phenomenon of the dimensions of Bott-Chern cohomology groups and Aeppli cohomology groups