ACR FLC HAS ALTDEV DURING DEP FROM PIT.

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ALTDEV OF +500 FT INDUCED BY ATC DEP. DURING OUR TKOF PHASE; WE HAD A PROB WITH OUR XPONDER CODE. IT WAS NOT REGISTERING TO ATC. WE WERE GIVEN RWY HDG TO 4000 FT. WHILE CLBOUT OUT; COMPLETING AFTER TKOF CHKLIST; DEALING WITH ICING CONDITIONS BY TURNING ON DEICE SYS; ATC REPEATEDLY DEMANDED WE RECTIFY OUR XPONDER PROB. AS PNF; I WAS JUGGLING WITH 3 THINGS HERE. ATC'S DEMANDS CAUSED DISTR FROM COMPLETING OUR TASK AT HAND; WHICH WAS TO COMPLETE TKOF PROFILE CLR OF ICE. THE DEMANDS OF ATC EVEN BROUGHT THE PF INTO THE SIT WHICH CAUSED HIM TO FLY THROUGH ASSIGNED ALT OF 4000 FT. ATC SAID WE WERE 4500 FT. SINCE ATC HAS CLRED US TO 4000 FT; I DON'T UNDERSTAND THE PANIC OF BEING RADAR IDENTED BEFORE THAT. ONCE LEVEL OR THEREABOUTS; THEY CAN DEMAND THESE THINGS BECAUSE AT THAT POINT; THE MOST IMPORTANT CHKLIST IS COMPLETE. DEP WAS ON OUR CASE WHEN WE WERE ONLY 1000 FT INTO THE CLB. TWR TELLS YOU TO SWITCH TO DEP ALMOST RIGHT AWAY. I GUESS WHEN WE CHK IN WITH DEP; THEY ASSUME OUR TKOF CHKLIST IS COMPLETE. SOMETIMES THEY WILL ASK IF YOU ARE WITH THEM BEFORE YOU CALL THEM. DEP SHOULD WAIT FOR DEPARTING ACFT TO CALL THEM FIRST AND SHOULD NOT HASSLE CREWS BEFORE LEVELING OFF AT ASSIGNED ALTS.