  A series of symmetry-protected topological(SPT) and trivial spin-gap phases
in the spin-1/2 ferromagnetic--antiferromagnetic alternating Heisenberg chain
with alternating next-nearest-neighbour interaction are investigated using two
kinds of entanglement spectra defined by different divisions of the whole
chain. In the case one of the next-nearest-neighbor interaction vanishes, the
model reduces to the $\Delta$-chain in which a series of spin-gap phases are
found in J. Phys. Soc. Jpn. 77, 044707 (2008). From the degeneracy of the
entanglement spectra, these phases are identified as the SPT and trivial
phases. It is found that the ground state phases boundaries are insensitive to
the strength of the alternation in next-nearest neighbor interaction. These
results are consistent with the analysis based on the nonlinear $\sigma$ model
and exact solution on the ferromagnetic-nonmagnetic phase boundary.
