A flight instructor reported a NMAC while practicing steep spirals.

Narrative

I am a Flight Instructor. My commercial student and I were doing a training flight involving the commercial maneuvers. The maneuver we were doing when the incident occurred was steep spirals. He was setting up for the maneuver; he did clearing turns; we scanned the area for traffic and we both visually verified the area was clear and confirmed using the traffic map on our avionics (ADS-B in). He began the maneuver; and as he was doing it; I was looking outside for traffic that may come up unexpectedly and also verifying with the traffic map. He was on his last turn about to complete the maneuver when I noticed an aircraft pop up unexpectedly on our traffic map 100 feet below and to the left of us. We took action to move away by climbing up and to the right. After we turned away; I was able to see an aircraft. After landing at LUK; I talked with other instructors and admin. The aircraft we were flying had been in maintenance for ADS-B issues before; and was presumably fixed. To prevent a recurrence; I as an instructor can take action to be more situationally aware; such as knowing where hotspots are in the practice area and of course using the see and avoid method and using ADS-B in as a back up resource.