  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.
