Small transport pilot reported the magnetic heading indicators on both PFDs disagreed by more than 5 degrees during departure climb at LGA; resulting in a track deviation from the SID. The indicators realigned after level-off.

Narrative

My Captain and I lined up on Runway 13 at LGA for departure. Once on the runway; waiting for takeoff clearance; the crew ran through standard call-outs; which include 'assigned runway confirmed; heading checks'. It was clear that this was the assigned Runway 13; as the numbers on the pavement confirmed that. However; our gyroscopic and synthetic vision equipment did not support that we were on a heading of 134 degrees; the charted runway heading for Runway 13. The runway information tab on our charts warned us of potential magnetic anomalies when lined up for departure on Runway 13; which the crew was aware of; so we proceeded to standby for our takeoff clearance from ATC. Our IFR clearance had us flying a SID; the LGA7 departure Whitestone climb which required us to turn to specific headings upon becoming clear of obstacles after takeoff; and reaching 2.5 DME from the LGA VOR. Once airborne; the magnetic heading indicators on our aircraft had not corrected themselves; and were more that 5 degrees off of each other; which raised the heading mis-compare flag on both mine and my Captain's PFD. After receiving a few more heading instructions from ATC during the departure phase; we had reduced the workload to allow bringing up the heading issue with ATC. After this; we were told what ATC saw our heading as; and used that to cross check with the instrumentation in the aircraft. Once level; the headings slowly began to correct themselves and realigned correctly. Being aware of the magnetic anomaly on Runway 13 at LGA prevented the crew from taking more decisive action when the equipment stopped working correctly; which caused the SID to be flown slightly off course than what it is charted to be. During this situation; we should have reported the loss of accurate magnetic heading indication to ATC sooner; as the New York airspace is very crowded and the flying of a SID into busy airspace has the potential to cause aircraft separation issues. Had ATC known about the issue sooner; we could have been issued NO-GYRO vectors to prevent the potential loss of separation between other aircraft; had there been more in the area at that time. Luckily on this day it was VMC conditions; with haze not really affecting visibility at the lower altitudes when this occurred. In the future; understanding the difference between a slight magnetic anomaly and a larger magnetic heading fluctuation would help the crew decide that canceling the takeoff clearance and using an intersection departure would help reduce the chances of a situation like this happening again.