  Nuclei in the $A\approx100$ region exhibit intricate shape-evolution and
configuration crossing signatures. Exploring both even-even and their adjacent
odd-mass nuclei gives further insight on the emergence of deformation and
shape-phase transitions. We employ the algebraic frameworks of the interacting
boson model with configuration mixing and the new interacting boson-fermion
model with configuration mixing in order to investigate the even-even zirconium
with neutron number 52-70 ($^{40}$Zr) and odd-mass niobium ($_{41}$Nb) isotopes
with 52-62. We compare between the evolution in energy levels, configuration
and symmetry content of the wave functions, two neutron separation energies and
$E2$ transition rates. The comparisons between the two chains of isotopes
denote the occurrence of intertwined quantum phase transitions (IQPTs) in both
chains. Such a situation occurs when two configurations, normal and intruder,
cross through the critical point of a Type II quantum phase transition (QPT),
and the intruder configuration undergoes on its own a Type I shape-evolution
QPT from a spherical shape (weak coupling scenario) to axially deformed rotor
(strong coupling scenario) in the Zr (Nb) isotopes.
