  We study and compare the sensitivity of multiple non-Markovianity indicators
for a qubit subjected to general phase-covariant noise. For each of the
indicators, we derive analytical conditions to detect the dynamics as
non-Markovian. We present these conditions as relations between the
time-dependent decay rates for the general open system dynamics and its
commutative and unital subclasses. These relations tell directly if the
dynamics is non-Markovian w.r.t.~each indicator, without the need to explicitly
derive and specify the analytic form of the time-dependent coefficients.
Moreover, with a shift in perspective, we show that if one assumes only the
general form of the master equation, measuring the non-Markovianity indicators
gives us directly non-trivial information on the relations between the unknown
decay rates.
