  In this article we consider spherical hypersurfaces in $\mathbb C^2$ with a
fixed Reeb vector field as 3-dimensional Sasakian manifolds. We establish the
correspondence between three different sets of parameters, namely, those
arising from representing the Reeb vector field as an automorphism of the
Heisenberg sphere, the parameters used in Stanton's description of rigid
spheres, and the parameters arising from the rigid normal forms. We also
geometrically describe the moduli space for rigid spheres, and provide
geometric distinction between Stanton's hypersurfaces and those found by Ezhov
and Schmalz. Finally, we determine the Sasakian automorphism groups of the
rigid spheres and detect the homogeneous Sasakian manifolds among them.
