  Relative motion effects have long been known to ``contaminate'' the
observations. In fact, when looking back to the history of astronomy, one finds
a number of examples where relative motions have led to a gross
misinterpretation of reality. Using relativistic cosmological perturbation
theory it was shown that observers living inside bulk-flow domains that expand
slightly slower than their surroundings, can have the illusion of cosmic
acceleration, while the host universe is actually decelerating. This claim was
originally based on studies of a perturbed tilted Einstein-de Sitter model,
primarily for mathematical simplicity. Nevertheless, nothing really changed
when the background universe was replaced by a Friedmann cosmology with nonzero
pressure and spatial curvature. This raised the possibility that the
peculiar-motion effect on the deceleration parameter, as measured locally by
the bulk-flow observers, may be generic and independent of the specifics of the
host universe. Here, we investigate this possibility, by extending the earlier
studies to perturbed Bianchi cosmologies. We find that the picture remains
unchanged, unless the Bianchi background has unrealistically high anisotropy.
The peculiar-motion effect on the deceleration parameter, as measured by the
relatively moving observers, is essentially the same with that reported earlier
in a perturbed Einstein-de Sitter universe and in the rest of its Friedmann
counterparts.
