  We study the zero-temperature transport properties of one-dimensional
normal-superconductor (NS) junctions with topological superconductors across
their topological transitions. Working within the Blonder-Tinkham-Klapwijk
(BTK) formalism generalized for topological NS junctions, we analytically
calculate the differential conductance for tunneling into two models of a
topological superconductor: a spinless intrinsic $p$-wave superconductor and a
spin-orbit-coupled $s$-wave superconductor in a Zeeman field. In both cases we
verify that the zero-bias conductance is robustly quantized at $2e^2/h$ in the
topological regime, while it takes nonuniversal values in the non-topological
phase. The conductance spectra in the topological state develops a peak at zero
bias for certain parameter regimes, with the peak width controlled by the
strength of spin-orbit coupling and barrier transparency.
