Pressure errors (i.e. errors in the measurement of pitot and static pressure) are specific to the aircraft so we have to allow for them. Instrument error is specific to the instrument so we have to get the instrument calibrated and take it into account. Having corrected the indicated airspeed for these two errors we have calibrated airspeed.

However small at take off speed we should correct for the effect of compressibility and that will give us equivalent airspeed.

For a given weight and configuration the take off speed will depend on the density of the air so we don't correct for that hence the aircraft will take off at the same EAS.