On local-to-global spectral sequences for the cohomology of diagrams
  The aim of this paper is to construct and examine three candidates for local-to-global spectral sequences for the cohomology of diagrams of algebras with directed indexing. In each case, the $E^2$ -terms can be viewed as a type of local cohomology relative to a map or an object in the diagram. 
David Blanc, Mark W. Johnson, and James M. Turner