  The cores of massive galaxy clusters, where hot gas is cooling rapidly,
appear to undergo cycles of self-regulating energy feedback, in which AGN
outbursts in the central galaxies episodically provide sufficient heating to
offset much of the gas cooling. We use deep integral-field spectroscopy to
study the optical line emission from the extended nebulae of three nearby
brightest cluster galaxies and investigate how they are related to the
processes of heating and cooling in the cluster cores. Two of these systems,
Abell 3581 and Sersic 159-03, appear to be experiencing phases of feedback that
are dominated by the activity and output of a central AGN. Abell 3581, shows
evidence for significant interaction between the radio outflows and the optical
nebula, in addition to accretion flows into the nucleus of the galaxy. X-ray
and radio data show that Sersic 159-03 is dominated by the feedback of energy
from the central AGN, but the kinematics of the optical nebula are consistent
with infall or outflow of material along its bright filaments. The third
system, 2A 0335+096, is dominated by mass accretion and cooling, and so we
suggest that it is in an accumulation phase of the feedback cycle. The outer
nebula forms a disk-like structure, ~14 kpc in radius, that rotates about the
central galaxy with a velocity amplitude of ~200 km/s. Overall, our data are
consistent with ongoing AGN-driven feedback cycles occurring in these systems.
