  Recent observations of galaxy clusters and groups with misalignments between
their central AGN jets and X-ray cavities, or with multiple misaligned
cavities, have raised concerns about the jet - bubble connection in cooling
cores, and the processes responsible for jet realignment. To investigate the
frequency and causes of such misalignments, we construct a sample of 16 cool
core galaxy clusters and groups. Using VLBA radio data we measure the
parsec-scale position angle of the jets, and compare it with the position angle
of the X-ray cavities detected in Chandra data. Using the overall sample and
selected subsets, we consistently find that there is a 30% - 38% chance to find
a misalignment larger than $\Delta\Psi = 45^{\circ}$ when observing a
cluster/group with a detected jet and at least one cavity. We determine that
projection may account for an apparently large $\Delta\Psi$ only in a fraction
of objects ($\sim$35%), and given that gas dynamical disturbances (as sloshing)
are found in both aligned and misaligned systems, we exclude environmental
perturbation as the main driver of cavity - jet misalignment. Moreover, we find
that large misalignments (up to $\sim90^{\circ}$) are favored over smaller ones
($45^{\circ}\leq\Delta\Psi\leq70^{\circ}$), and that the change in jet
direction can occur on timescales between one and a few tens of Myr. We
conclude that misalignments are more likely related to actual reorientation of
the jet axis, and we discuss several engine-based mechanisms that may cause
these dramatic changes.
