  We study the phase transition between a trivial and a time-reversal-invariant
topological superconductor in a single-band system. By analyzing the interplay
of symmetry, topology and energetics, we show that for a generic normal state
band structure, the phase transition occurs via extended intermediate phases in
which even- and odd-parity pairing components coexist. For inversion-symmetric
systems, the coexistence phase spontaneously breaks time-reversal symmetry. For
noncentrosymmetric superconductors, the low-temperature intermediate phase is
time-reversal breaking, while the high-temperature phase preserves
time-reversal symmetry and has topologically protected line nodes. Furthermore,
with approximate rotational invariance, the system has an emergent $U(1) \times
U(1)$ symmetry, and novel topological defects, such as half vortex lines
binding Majorana fermions, can exist. We analytically solve for the dispersion
of the Majorana fermion and show that it exhibit small and large velocities at
low and high energies. Relevance of our theory to superconducting pyrochlore
oxide Cd$_2$Re$_2$O$_7$ and half-Heusler materials is discussed.
