  The dynamics of baryon-antibaryon annihilation and reproduction ($B{\bar B}
\leftrightarrow 3 M$) is studied within the Parton-Hadron-String Dynamics
(PHSD) transport approach for Pb+Pb and Au+Au collisions as a function of
centrality from lower Super Proton Synchrotron (SPS) up to Large Hadron
Collider (LHC) energies on the basis of the quark rearrangement model (QRM). At
Relativistic Heavy-Ion Collider (RHIC) energies we find a small net reduction
of baryon-antibaryon ($B {\bar B}$) pairs while for the LHC energy of
$\sqrt{s_{NN}}$ = 2.76 GeV a small net enhancement is found relative to
calculations without annihilation (and reproduction) channels. Accordingly, the
sizeable difference between data and statistical calculations in Pb+Pb
collisions at $\sqrt{s_{NN}}$= 2.76 TeV for proton and antiproton yields
\cite{53}, where a deviation of 2.7 $\sigma$ was claimed by the ALICE
Collaboration, should not be attributed to a net antiproton annihilation. This
is in line with the observation that no substantial deviation between the data
and statistical hadronization model (SHM) calculations is seen for
antihyperons, since according to the PHSD analysis the antihyperons should be
modified by the same amount as antiprotons. As the PHSD results for particle
ratios are in line with the ALICE data (within error bars) this might point
towards a deviation from statistical equilibrium in the hadronization (at least
for protons/antiprotons). Furthermore, we find that the $B {\bar B}
\leftrightarrow 3 M$ reactions are more effective at lower SPS energies where a
net suppression for antiprotons and antihyperons up to a factor of 2 -- 2.5 can
be extracted from the PHSD calculations for central Au+Au collisions.
