  We analyze how the crust equation of state affects several neutron star
properties and how it impacts on possible constraints inferred from
astrophysical observations. Using three distinct crusts, we generate three sets
of model-independent equations of state describing stellar matter from a Taylor
expansion around saturation density. The equations of state are
thermodynamically consistent, causal, and compatible with astrophysical
observations. The relations between the tidal deformability $\Lambda$ and
compactness $C$, Love number $k_2$ and radius of neutron star with mass $M$ are
studied, and the effect of the crust equation of state on these relations
analyzed. In most of the relations, the impact of the crust equation of state
is not larger that 2\%. If, however, a fixed neutron star mass is considered,
the relation between the tidal deformability and the radius depends on the
crust. We have found that the relation $\Lambda_{M_i} = \alpha R_{M_i}^{\beta}$
becomes almost exact and crust independent for massive neutron stars. It is
shown that it is possible to determine the tidal deformability of an
1.4$M_\odot$ star from the GW179817 effective tidal deformability
$\tilde\Lambda$ with an accuracy of at least $\approx 10\%$. A high correlation
between $\tilde\Lambda$ and the radius of the most massive star of the neutron
star binary was confirmed, however, it was demonstrated that the crust has an
effect of $\approx 14\%$ on this relation. We have found that the relation
$\Lambda_1/\Lambda_2=q^a$ depends on $M_{\text{chirp}}$ as $a\sim
\sqrt{M_{\text{chirp}}}$.
