  We show that two smooth nearby Riemannian metrics can be glued interpolating
their scalar curvature. The resulting smooth metric is the same as the starting
ones outside the gluing region and has scalar curvature interpolating between
the original ones. One can then glue metrics while maintaining inequalities
satisfied by the scalar curvature. We also glue asymptotically Euclidean
metrics to Schwarzschild ones and the same for asymptotically Delaunay metrics,
keeping bounds on the scalar curvature, if any. This extend the Corvino gluing
near infinity to non-constant scalar curvature metrics.
