The first transformation is an Achmatowicz rearrangement, followed by protection and selective reduction; the last is a Johnson-Claisen rearrangement.
The acetal protects the other oxygenated position during hydride reduction. The orthoester transfers an acetate-derived two-carbon unit through a ketene acetal; it does not directly substitute the allylic OH with an intact acetate ion.
Figure 1.
Atom maps for the allylic ketene-acetal and ammonium-ylide rearrangements
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