  We consider some metrics and weak metrics defined on the Teichmueller space
of a surface of finite type with nonempty boundary, that are defined using the
hyperbolic length spectrum of simple closed curves and of properly embedded
arcs, and we compare these metrics and weak metrics with the Teichm\"uller
metric. The comparison is on subsets of Teichm\"uller space which we call
"$\epsilon_0$-relative $\epsilon$-thick parts", and whose definition depends on
the choice of some positive constants $\epsilon_0$ and $\epsilon$. Meanwhile,
we give a formula for the Teichm\"uller metric of a surface with boundary in
terms of extremal lengths of families of arcs.
