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