The structure of deformed double complexes on the Iwasawa manifold

The Kuranishi family of the Iwasawa manifold give rise naturally to a family of (deformed) double complexes. By using the structure theorem of double complexes due to Stelzig and Qi-Khovanov, we show there are exactly $3$ isomorphism types in this family and determine explicitly structures of these $3$ types. As an application, we computed the Fr\"olicher spectral sequence for each fiber in the Kuranishi family of the Iwasawa manifold.