$A_{\infty}$-structures for Bott-Chern and Aeppli cohomologies

In this article, we introduce certain arity-3 operations on complex manifolds arising from homotopy transfer theory. Such operations are related to the triple ABC-Massey products from Bott-Chern to Aeppli cohomology. We present a package for computing such products as well as other cohomological and homotopical invariants for complex nilmanifolds and give some examples.