  We investigate the ground-state phase diagram of the bond-alternating $S=2$
quantum spin chain with the $XXZ$ and on-site anisotropies. For the on-site
anisotropies, in addition to the popular $D_2 \sum_j (S_j^z)^2$ term, we
consider the $D_4 \sum_j (S_j^z)^4$ term. Mainly we use the exact
diagonalization and the level spectroscopy analysis. We show that the Haldane
state, large-$D$ state and the Dimer2 state belong to the same trivial phase,
by finding the existence of adiabatic paths directly connecting these states
without the quantum phase transition. Similarly, we show that the
intermediate-$D$ state and the Dimer1 state belong to the same symmetry
protected topological phase.
