  We investigate the deformation of an $L_\infty$ structure that encodes the
geometric information about a smooth vector bundle. We establish that this
specific type of deformation endows the bundle with a Lie algebroid structure.
Additionally, we compute the Atiyah class and Atiyah-Chern classes in the
geometrically deformed case. The precise relationship between the first
Atiyah-Chern class and the modular class is shown. In the case of action Lie
algebroids, the Atiyah-Chern classes at the leading order are given by the
equivariant Chern characters.
