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We provide further techniques to study the Dolbeault and Bott-Cherncohomologies of deformations of solvmanifolds by means of finite-dimensionalcomplexes. By these techniques, we can compute the Dolbeault and Bott-Cherncohomologies of some complex solvmanifolds, and we also get explicit examples,showing in particular that either the $\partial\overline{\partial}$-Lemma orthe property that the Hodge and Fr\"olicher spectral sequence degenerates atthe first level are not closed under deformations.

Cohomologies of deformations of solvmanifolds and closedness of some properties