  We evaluate the redshift distribution of binary black hole (BBH), black hole
- neutron star binary (BHNS) and binary neutron star (BNS) mergers, exploring
the main sources of uncertainty: star formation rate (SFR) density, metallicity
evolution, common envelope, mass transfer via Roche lobe overflow, natal kicks,
core-collapse supernova model and initial mass function. Among binary evolution
processes, uncertainties on common envelope ejection have a major impact: the
local merger rate density of BNSs varies from $\sim{}10^3$ to $\sim{}20$
Gpc$^{-3}$ yr$^{-1}$ if we change the common envelope efficiency parameter from
$\alpha_{\rm CE}=7$ to 0.5, while the local merger rates of BBHs and BHNSs vary
by a factor of $\sim{}2-3$. The BBH merger rate changes by one order of
magnitude, when $1 \sigma$ uncertainties on metallicity evolution are taken
into account. In contrast, the BNS merger rate is almost insensitive to
metallicity. Hence, BNSs are the ideal test bed to put constraints on uncertain
binary evolution processes, such as common envelope and natal kicks. Only
models assuming values of $\alpha_{\rm CE}\gtrsim{}2$ and moderately low natal
kicks (depending on the ejected mass and the SN mechanism), result in a local
BNS merger rate density within the 90% credible interval inferred from the
second gravitational-wave transient catalogue.
