  We aim to study the main properties of a volume-limited unbiased sample of
well-characterized semi-regular variables (SRs) in order to clarify important
issues, such as the formation of axially symmetric planetary nebulae (PNe) from
spherical circumstellar envelopes (CSEs), which takes place during the
mass-loss process along the AGB phase. We present new high-S/N IRAM 30m
observations of the 12CO J=2-1, J=1-0, and 13CO J=1-0 lines, in a
volume-limited sample of SRs. We analyzed the data by characterizing the main
properties of the CSEs. The 12CO J=2-1 data were used to study the profiles,
while the 12CO J=1-0 data were used to estimate mass-loss rates for the
complete sample. We have classified the sources into four groups according to
the different profiles and final gas expansion velocities. Type 1 and 2
profiles are broad and narrow symmetric lines, respectively. Type 3 profiles on
the contrary are strange profiles with very pronounced asymmetries. Finally,
type 4 profiles are those showing two different components: a narrow line
profile superimposed on a broad pedestal component. Interestingly, we report a
moderate correlation between mass-loss rates and 12CO J=1-0/J=2-1 line
intensity ratios for O-rich SRs, suggesting a different behaviour between C-
and O-rich SRs. Using SHAPE+shapemol, we find a unified simple model based on
an oblate spheroid placed in different orientations that may explain all the
12CO profiles in the sample, indicating that the gas expansion is in general
predominantly equatorial. Moreover, in order to explain the type 4 profiles, we
define an extra component which may somehow be a biconical structure or
similar. Type 1 and 2 profiles, curiously, may also be explained by standard
spherically symmetric envelopes. We conclude that most circumstellar shells
around SRs show axial, strongly nonspherical symmetry.
