Injection of a vaccine into the body creates an immune response against the particular antigen used in the vaccine. Mucosal vaccination however has been shown to also confer cross protection against other viral or bacterial strains.
A nasal vaccine has the potential to provide cross protection and elicit protection against disease, even if it does not contain exactly the same strain of the pathogen that is currently circulating. Diseases where this can be the case are e.g. influenza and HIV.