All of this would come to an abrupt end if there was a complete shutdown. Regarding passenger flights, both FAI and ANC are essential for Pacific and Polar air routes.
These airports are sometimes used for emergency landings, refueling, and diversion for flights between North America and Asia or the US and Europe.
If they were closed, incoming passenger planes would have to change their routes, which would lengthen trip durations and cause traffic at other airports.
Until the ash cloud clears, which may take hours or days depending on how long the eruption lasts, all planes leaving from these airports would be grounded.
Mount Spurr might thereby affect transit and freight operations, causing problems that run far beyond the Alaskan border. This volcano last had three consecutive explosive episodes.