Large-scale eddies responsible for much of the midlatitude weather develop through a standard lifecycle. First, temperature gradients increase due to differences in the equator-to-pole heating. Eddies grow to mix the atmosphere, transporting (fluxing) heat towards the poles. The eddies intensify, measured by eddy kinetic energy (EKE), then break and flux their momentum to the background east-west or U wind (the jet stream). To measure these steps in a simple way, previous studies calculated two types of modes of variability, called annular modes (AM), as they are created by averaging across latitudes. The baroclinic AM measures the changes in zonal-mean EKE in time, and the barotropic AM measures the U wind. Simplifying the description of the eddy lifecycle helps with predictions of clouds and precipitation. Previously, the two AMs were not correlated, and each mode only mapped onto two of the four stages of the eddy lifecycle: the baroclinic AM onto the eddy heat fluxes and EKE and the barotropic AM onto the eddy momentum fluxes and U wind. We unify the first and second halves of the lifecycle by redefining eddies from zonal deviations to time deviations. This change links the baroclinic and barotropic AMs through all four lifecycle stages.