Lithium aluminum hydride reduces the anhydrides to alcohols. In a first stage the molecule breaks, forming aldehyde and carboxylate which are in turn reduced to alcohols.

reduction-anhydrides

The reaction mechanism occurs in the following stages

Stage 1 .
hydride addition

reduction-anhydrides

Stage 2 .
acetate removal

reduction-anhydrides

Stage 3. Reduction of aldehyde and carboxylate to alcohol

reduction-anhydrides