  This work aims at determining the impact of slow to moderate rotation on the
regular patterns often present in solar-like oscillation spectra. We focus on
the well-known asteroseismic diagnostic echelle diagrams, examining how
rotation may modify the estimates of the large and small spacings, as well as
the identification of modes. We illustrate the work with a real case: the
solar-like star $\eta$ Bootis. The modeling takes into account rotation effects
on the equilibrium models through an effective gravity and on the oscillation
frequencies through both perturbative and non-perturbative calculations. We
compare the results of both type of calculations in the context of the regular
spacings (like the small spacings and the scaled small spacings) and echelle
diagrams. We show that for echelle diagrams the perturbative approach remains
valid for rotational velocities up to 40-50 km/s. We show that for the
rotational velocities measured in solar-like stars, theoretical oscillation
frequencies must be corrected up to the second-order in terms of rotation rate,
including near degeneracy effects. For rotational velocities of about 16 km/S
and higher, diagnostics on large spacings and on modal identification through
echelle diagrams can be significantly altered by the presence of the $m\neq0$
components of the rotationally split modes. We found these effects to be
detectable in the observed frequency range. Analysis of the effects of rotation
on small spacings and scaled small spacings reveals that these can be of the
order of, or even larger than surface effects, typically turbulence,
microscopic diffusion, etc. Furthermore, we show that scaled spacings are
significantly affected by stellar distortion even for small stellar rotational
velocities (from 10-15 km/s) and therefore some care must be taken when using
them as indicators for probing deep stellar interiors.
