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.
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