We search for bright Ly$rm alpha$ emitters among Spitzer SMUVS galaxies at z > 2.9 with homogeneous MUSE data. Although it only covers a small region of COSMOS, MUSE has the unique advantage of providing spectral information over the entire field, without the need of target pre-selection. This gives an unbiased detection of all the brightest Ly$rm alpha$ emitters among SMUVS sources, which by design are stellar-mass selected galaxies. Within the studied area, ~14% of the SMUVS galaxies at z > 2.9 have Ly$rm alpha$ fluxes F$rm _lambda$ > 7 x 10$^{-18}$ erg s$^{-1}$ cm$^{-2}$. These Ly$rm alpha$ emitters are characterized by three types of emission, 47% show a single line profile, 19% present a double peak or a blue bump and 31% show a red tail. One object (3%) shows both a blue bump and a red tail. We also investigate the spectral energy distribution (SED) properties of the SMUVS MUSE-detected galaxies and MUSE non-detections. After stellar-mass matching both populations, we find that MUSE detected galaxies have generally lower extinction than SMUVS-only objects, while there is no clear intrinsic difference in the mass and age distributions. For the MUSE-detected SMUVS galaxies, we compare the instantaneous SFR lower limit given by Ly$rm alpha$ flux with its past average derived from SED fitting, and find evidence for rejuvenation in some of our oldest objects. We also study the spectra of those Ly$rm alpha$ emitters which are not detected in SMUVS in the same field. We find different distributions of the emission line profiles, which could be ascribed to the fainter Ly$rm alpha$ luminosities of the MUSE-only sources and an intrinsically different mass distribution. Finally, we search for the presence of galaxy associations. MUSEs integral coverage is 20 times more likely to find associations than all other existing spectral data in COSMOS, biased by target pre-selection.
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