Technically, no—you cannot fly "over" or through Class B airspace without a functioning Mode C or Mode S transponder (and ADS-B Out) unless you have received specific, prior authorization from Air Traffic Control (ATC). Under FAA regulations (14 CFR 91.215), a transponder with altitude-reporting capability is required within the "Mode C Veil," which is a 30-nautical-mile radius extending from the surface to 10,000 feet MSL around the nation's busiest airports. Even if you are flying above the ceiling of the Class B (which is usually 10,000 feet), you are still within the lateral boundaries where ADS-B and transponders are mandatory. The only exception for flying without this equipment is if the aircraft was originally certificated without an electrical system (like certain vintage Piper Cubs or gliders), and even then, they are generally restricted from entering the Mode C Veil or Class B airspace itself. If your transponder fails in flight, you must immediately notify ATC, and they may, at their discretion, allow you to continue to your destination, but you cannot legally plan a flight through or over these areas without the required equipment.