  The Turaev-Viro state sum model provides a covariant spin foam quantization
of three-dimensional Riemannian gravity with a positive cosmological constant
{\Lambda}. We complete the program to canonically quantize the theory in the BF
formulation using the formalism of Loop Quantum Gravity. In particular, we show
first how quantum group structures arise from the requirement of the constraint
algebra to be anomaly free. This allows us to generalize the construction of
the physical scalar product, from the {\Lambda} = 0 case, in presence of a
positive {\Lambda}. We prove the equivalence between the covariant and
canonical quantizations by recovering the spin foam amplitudes.
