Final answer:
The provided text does not clearly articulate how Percy and Grover travel back to New York City in the usual Percy Jackson series context but presents a fantastical journey involving a limousine that ascends into the air and moves through a gulch.
Step-by-step explanation:
In the excerpts provided, Percy and Grover's mode of travel back to New York City for the summer is not specified within the context of typical Percy Jackson books. Instead, the passages detail different characters and scenarios that seem to blend early 20th-century settings with elements of fantasy.
For instance, Percy and another character are seen traveling in a limousine that ascends into the air with cables and moves through a rough gulch with the help of a searchlight, suggesting a rather fantastical journey that defies reality. The content provided doesn't fit within the canonical Percy Jackson universe.
The subjects cover various transportation means ranging from limousines to air tubes, with some settings in Canada and Niagara Falls, creating an ambiguous and unusual travel narrative.