  We give an $L_\infty$-interpretation of the classification, obtained in
[AP2], of the formal deformations of a family of exact Poisson structures in
dimension three. We indeed obtain again the explicit formulas for all the
formal deformations of these Poisson structures, together with a classification
in the generic case, by constructing a suitable quasi-isomorphism between two
$L_\infty$-algebras, which are associated to these Poisson structures.
