  Due to non-perturbative quantum gravitational effects, the classical big bang
singularity is replaced by a quantum big bounce of the mean scale factor in
loop quantization of Bianchi-I spacetime. An important issue is to understand
various differences in the physical properties of the spacetime across the
bounce. We investigate this issue in the context of various geometrical
structures, identified by Kasner exponents of the metric, which arise on
approach to the singularity in the classical theory. Using effective spacetime
description of Bianchi-I model in loop quantum cosmology with dust, radiation
and stiff matter, we find that as in the classical theory, geometrical
structures such as a cigar or a pancake form, but they are finite and
non-singular. Depending on the initial conditions of matter and anisotropies,
different geometric structures are possible in the pre- and post-bounce phases
in physical evolution. Thus, quantum gravitational effects can cause a Kasner
transition in Bianchi-I spacetime, which is not possible at the classical
level. Interestingly, we find that not all transitions are allowed at the level
of effective dynamics in loop quantum cosmology. We find the selection rules
and underlying conditions for all allowed and forbidden transitions. Selection
rules suggest that for a given set of initial conditions on anisotropies,
occurrence of Kasner transitions follows a distinct pattern, and certain
transitions are more favored than others.
