Pilot reported a NMAC during a descent with another aircraft that was practicing maneuvers in the area.
Synopsis
Pilot reported a NMAC during a descent with another aircraft that was practicing maneuvers in the area.
Narrative
I was on a direct flight from ZZZ2 to ZZZ1 in ZZZ airspace with flight following. Descending approximately 300 fpm from 7500 ft.; I once slowed my descent for crossing traffic below; and a second time leveled at 5500 ft. for the aircraft involved. At the time my TCAS was showing that aircraft 800 ft. below at approximately 4700 ft.Unfortunately the CFI indicated he never saw me visually nor on his equipment as he and a student were practicing power on stalls. The EFB indicated they were climbing at over 900 fpm at approximately 160 mph when they got dangerously close to my aircraft flying level at 5500 ft.My equipment did give me a traffic warning at which time I immediately looked to my left knowing his path was east bound (mine being north of course). I expected to see him below my position and was surprised to see him at my altitude a few hundred feet to my left. It was then that they apparently saw me and banked right. A couple seconds after I made eye contact and the aircraft banked left a very nervous ATC controller came on and warned me to climb immediately due to traffic. Fortunately I was able to relieve the controller by stating I had eyes on the traffic. To my knowledge the other aircraft was not utilizing any flight following; and in email correspondence the other pilot indicated they didn't see me on their equipment nor visually when they commenced their climb. In retrospect; the CFI/Owner should certainly have his equipment checked immediately; as there is no reason I shouldn't have shown up on his equipment broadcasting ADS-B out and being in ATC radar. Moreover; even when not going from point A to B I believe it's even more important to contact ATC for a unique code as predictability of training aircraft altitude and direction is limited vs an aircraft flying from point A to B. Had he been in the system; it's possible ATC could have given him a heads up sooner. Granted their warning to me was late; but of course flight following guidance is on a time available and it was a nice sunny day so lots of activity so not faulting ATC.Hope that the best lesson is a reminder to a very seasoned pilot; from a relatively new but careful private pilot; to utilize all your resources for traffic avoidance; especially on a nice day.
Second reporter narrative
During multiengine training with a new student we were performing Takeoff/Departure stalls. We had previously checked for traffic visually and with the ADS-B on the EFB map on our mounted iPad. While we were in a climbing right turn we saw another aircraft at our 12 o'clock position and continued our right turn to miss him and leveled off. There were no warnings from the TIS on the Garmin 430 or from the iPad. After we passed him I did see him on ADS-B on the iPad.
Source: NASA Aviation Safety Reporting System (public domain). Reports are voluntary submissions and are not verified by NASA.