  We consider the loop quantization of the (diagonal) Bianchi type IX
cosmological model. We explore different quantization prescriptions that extend
the work of Wilson-Ewing and Singh. In particular, we study two different ways
of implementing the so-called inverse triad corrections. We construct the
corresponding Hamiltonian constraint operators and show that the singularity is
formally resolved. We find the effective equations associated with the
different quantization prescriptions, and study the relation with the isotropic
$k$=1 model that, classically, is contained within the Bianchi IX model. We use
geometrically defined scalar observables to explore the physical implications
of each of these theories. This is the first part in a series of papers
analyzing different aspects of the Bianchi IX model, with inverse corrections,
within loop quantum cosmology.
