Dynamic triggering has been commonly observed after large teleseismic events, but the physics behind it is still under debate. To broaden observations, we here focus on the dynamic triggering by regional earthquakes, that is, by events with magnitude lower than 6.2 at distances smaller than 600 km. The western part of the Corinth Rift (Greece) is characterized by intense seismic swarms and is therefore adapted to study such responses. The microseismicity rates before and after the transient perturbations are high enough to analyze 30 regional earthquakes out of the 59 occurring in 2013. More than 40% of those 30 events, including earthquakes with magnitude as small as 4.5, are associated with a significant seismicity rate increase. The triggerability primarily depends on the amplitude of the seismic waves. However, triggering is mainly observed when the seismic perturbations are orthogonal to the faults, which suggests that fluid pressurization is likely involved.