Applying a potential vorticity (PV) approach to observational analyses, the dynamic interaction between the troposphere and stratosphere during different phases of the Arctic Oscillation is diagnosed. We evaluate the typical structures and dynamic mechanisms of this interaction, focusing particularly on the transient feedback of stratospheric anomalies upon the tropospheric circulation. Lag regression techniques are used to isolate the time-evolving 3-D circulation anomalies associated with the Arctic Oscillation. The dynamical evolution is then diagnosed using PV and the invertibility principle. In particular, 3-D circulation anomalies are decomposed into separate parts associated with distinct PV anomaly features, permitting a diagnosis of far-field circulations associated with local PV structures. This allows an assessment of the dynamic interaction among separate PV anomaly features. PV analyses are complemented with traditional diagnoses such as spectral decomposition, E-P fluxes, and refractive index measures. Our results indicate that stratospheric PV anomalies make a significant contribution to the tropospheric zonal-mean flow associated with the Arctic Oscillation.