The relationship between shallow magma storage and flank injections in volcanic edifices is rarely documented. We analyse the time series of geodetic and seismic data collected at Piton de La Fournaise volcano (La Reunion) during 9 flank eruptions from 2000 to 2003. The data depicts how magma injections supplied flank eruptions at Piton de la Fournaise volcano, and allows to precisely determine the direction and duration of dike intrusions, indicating a two phases pattern, consistent over all the eruptions: 1) Fast vertical migration of the dyke (~2 m/s) from the magma chamber to the surface in 10 to 50 minutes, and 2) slower, lateral migration (0.2--0.8 m/s) in tens of minutes to hours controlled by the rift zone geometry.