We will present our study of the flux and spectral variability of the Crab above 100 MeV on different timescales ranging from days to weeks. In addition to the four main intense and day-long flares detected by AGILE and Fermi-LAT between Sept. 2007 and Sept. 2012, we find evidence for week-long and less intense episodes of enhanced gamma-ray emission that we call "waves". Statistically significant "waves" show timescales of 1-2 weeks, and can occur by themselves or in association with shorter flares. The Sept. - Oct. 2007 gamma-ray enhancement episode detected by AGILE shows both "wave" and flaring behavior.

We extend our analysis to the publicly available Fermi-LAT dataset and show that several additional "wave" episodes can be identified. We discuss the spectral properties of the September 2007 "wave"/flare event and show that the physical properties of the "waves" are intermediate between steady and flaring states. Plasma instabilities inducing "waves" appear to involve spatial distances $ l \sim 10^{16} \,$cm and enhanced magnetic fields $B \sim (0.5 - 1)\,$}mG.

Day-long flares are characterized by smaller distances and larger local magnetic fields. Typically, the deduced total energy associated with the "wave" phenomenon ($E_w \sim 10^{42} \, \rm erg$, where $E_w$ is the kinetic energy of the emitting particles) is comparable with that associated to the flares, and can reach a few percent of the total available pulsar spindown energy. Most likely, flares and waves are the product of the same class of plasma instabilities that we show acting on different timescales and radiation intensities.