  We study the superfluid transition in a quasi-two-dimensional Fermi gas with
a magnetic field tuning through a Feshbach resonance. Using an effective
two-dimensional Hamiltonian with renormalized interaction between atoms and
dressed molecules, we investigate the Berezinskii-Kosterlitz-Thouless
transition temperature by studying the phase fluctuation effect. We also take
into account the trapping potential in the radial plane, and discuss the number
and superfluid density distributions. These results can be compared to
experimental outcomes for gases prepared in one-dimensional optical lattices.
