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We perform an Observing System Simulation Experiment (OSSE), that simulates the satellite sampling and the mapping procedure on the sea surface of the high-resolution model CROCO-MED60v40, to investigate the reliability and the accuracy of the eddy detection. The main result of this study is a strong cyclone-anticyclone asymmetry of the eddy detection on the altimetry products AVISO/CMEMS in the Mediterranean Sea. Large scale cyclones having a characteristic radius larger than the local deformation radius are much less reliable than large scale anticyclones. We estimate that less than 60% of these cyclones detected on gridded altimetry product are reliable, while more than 85% of mesoscale anticyclones are reliable. Besides, both the barycenter and the size of these mesoscale anticyclones are relatively accurate. This asymmetry comes from the difference of stability between cyclonic and anticyclonic eddies. Large mesoscale cyclones often split into smaller sub mesoscale structures having a rapid dynamical evolution. The numerical model CROCO-MED60v40 shows that this complex dynamic is too fast and too small to be accurately captured by the gridded altimetry products. The spatio-temporal interpolation smoothes out this sub mesoscale dynamics and tends to generate an excessive number of unrealistic mesoscale cyclones in comparison with the reference field. On the other hand, large mesoscale anticyclones, which are more robust and which evolve more slowly, can be accurately tracked by standard altimetry products. We also confirm that the AVISO/CMEMS products induce a bias on the eddy intensity. The azimuthal geostrophic velocities are always underestimated for large mesoscale anticyclones. Plain Language Summary Altimetry satellite measurements are now used as a standard way to detect oceanic eddies on a regular and continuous basis. This study shows that cyclonic and anticyclonic eddies are not detected with the same accuracy. The reliability and the accuracy of detection of anticyclones is much higher than for cyclones in the Mediterranean Sea. Less than 60% of cyclonic eddies are correctly detected, whereas the position and size of large-scale anticyclones is relatively correct for 85% of them, even for observations provided in real time. Moreover, the intensity of large-scale eddies is systematically underestimated. These biases must be taken into accounts when using AVISO/CMEMS data for operational purposes especially in the Mediterranean Sea.