Equatorial observations in the Atlantic show three distinct vertical scales: quasi-barotropic eastward Extra-Equatorial Jets (EEJ), Equatorial Deep Jets (EDJ) of scale 500-800 m, and a smaller scale signal (50-100 m) of thin layers of well-mixed tracer fields. In the combined system of jets, westward EDJ correspond to zero-Potential Vorticity (PV) "niches," inside of which most of the thin well-mixed layers are found. Because of its correlation with zero-PV niches, the formation of layers is interpreted as due to inertial instability. The latter encompasses inertial barotropic instability due to meridional shear (either steady or parametric), baroclinic symmetric instability due to sloping isopyenals and vertical velocity shear, and effective-beta inertial instability due to the curvature of a westward jet at the equator. In very high resolution numerical simulations, where equatorial deep jets of 500-800 m vertical scale are produced, density layering is observed with a characteristic depth of mixing of about 50 m. A statistical analysis reveals that the well-mixed layers are located in zones of marginal inertial stability, mainly due to the vertical shear of zonal velocity and curvature of westward jets and therefore points toward a baroclinic symmetric instability mechanism and an effective-beta inertial instability.