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In this paper, we first provide an explicit procedure to glue togetherhereditary exact model structures for the recollement of exact categories. Tothat end, we use the notion of cotorsion pairs and we investigate the gluing ofcomplete hereditary cotorsion pairs along the recollement of exact categories.Moreover, we study liftings of recollements of hereditary exact modelstructures to recollements of their associated homotopy categories. This leadsto a new method to produce recollements of triangulated categories.Applications are given to contraderived categories, projective stable derivedcategories and stable categories of Gorenstein injective modules over an uppertriangular matrix ring.

Gluing and lifting exact model structures for the recollement of exact categories