  We consider some natural infinitesimal Einstein deformations on Sasakian and
3-Sasakian manifolds. Some of these are infinitesimal deformations of Killing
spinors and further some integrate to actual Killing spinor deformations. In
particular, on 3-Sasakian 7 manifolds these yield infinitesimal Einstein
deformations preserving 2, 1, or none of the 3 independent Killing spinors.
Toric 3-Sasakian manifolds provide non-trivial examples with integrable
deformation preserving precisely 2 Killing spinors. Thus the dimension of
Killing spinors is not preserved under Einstein deformations but is only upper
semi-continuous.
