We study the Gysin triangle in the triangulated category of mixed motives over a perfect field defined by Voevodsky. This study leads to the definition of the Gysin morphism of a projective morphism between smooth schemes, which in turn gives duality for motives of smooth projective schemes. We also define a motivic version of the coniveau spectral sequence and compute explicitly its differentials obtaining formulas analog to that of Quillen in K-theory. This computation is used to extend works of Bloch-Ogus on the coniveau filtration to the case of rigid cohomology - and more generally to the case of any mixed Weil cohomology theory in the sense introduced by D.C.Cisinski and the author.