  The $\theta$-deformed Hopf fibration $\mathbb{S}^3_\theta\to \mathbb{S}^2$
over the commutative $2$-sphere is compared with its classical counterpart. It
is shown that there exists a natural isomorphism between the corresponding
associated module functors and that the affine spaces of classical and deformed
connections are isomorphic. The latter isomorphism is equivariant under an
appropriate notion of infinitesimal gauge transformations in these contexts.
Gauge transformations and connections on associated modules are studied and are
shown to be sensitive to the deformation parameter. A homotopy theoretic
explanation for the existence of a close relationship between the classical and
deformed Hopf fibrations is proposed.
