  Generic resolution of singularities and geodesic completeness in the loop
quantization of Bianchi-II spacetimes with arbitrary minimally coupled matter
is investigated. Using the effective Hamiltonian approach, we examine two
available quantizations: one based on the connection operator and second by
treating extrinsic curvature as connection via gauge fixing. It turns out that
for the connection based quantization, either the inverse triad modifications
or imposition of weak energy condition is necessary to obtain a resolution of
all strong singularities and geodesic completeness. In contrast, the extrinsic
curvature based quantization generically resolves all strong curvature
singularities and results in a geodesically complete effective spacetime
without inverse triad modifications or energy conditions. In both the
quantizations, weak curvature singularities can occur resulting from
divergences in pressure and its derivatives at finite densities. These are
harmless events beyond which geodesics can be extended. Our work generalizes
previous results on the generic resolution of strong singularities in the loop
quantization of isotropic, Bianchi-I and Kantowski-Sachs spacetimes.
