  An E$_7$-Weierstrass model is conjectured to have eight distinct crepant
resolutions whose flop diagram is a Dynkin diagram of type E$_8$. In previous
work, we explicitly constructed four distinct resolutions, for which the flop
diagram formed a D$_4$ sub-diagram.
  The goal of this paper is to explore those properties of a resolved
E$_7$-model which are not invariant under flops. In particular, we examine the
fiber degenerations, identify the fibral divisors up to isomorphism, and study
violation of flatness appearing over certain codimension-three loci in the
base, where a component of the fiber grows in dimension from a rational curve
to a rational surface. For each crepant resolution, we compute the triple
intersection polynomial and the linear form induced by the second Chern class,
as well as the holomorphic and ordinary Euler characteristics, and the
signature of each fibral divisor. We identify the isomorphism classes of the
rational surfaces that break the flatness of the fibration. Moreover, we
explicitly show that the D$_4$ flops correspond to the crepant resolutions of
the orbifold given by $\mathbb{C}^3$ quotiented by the Klein four-group.
