Recent Solar Cycle 24 is characterized by the occurrence of three strong disturbances near an equinox. In this contribution, the responses of the ionosphere to the equinox storms in 2012, 2013 and 2015 driven by coronal mass ejections were analyzed. Due to the dynamic nature of changes in the ionosphere, the accuracy and resolution of existing global ionosphere models are often insufficient to reflect the storm-time effects in detail. Bearing this in mind, a new highly accurate and high-resolution regional ionosphere model was applied to study the response of this layer to severe geomagnetic storms over Europe. New regional total electron content (TEC) maps were derived exclusively from precise global navigation satellite systems (GNSS) carrier phase data. Although this study is based on space-geodetic technique, it was also carried out in relation to the observations provided from European ionosondes. In addition, the regional maps were compared to the final IGS Global Ionosphere Maps, where the new solution showed a better detail level. The results of storm-time temporal TEC changes provided by GNSS data were confirmed by NmF2 changes derived from ionosondes. Both data sources confirmed their high compatibility for studying the disturbed ionosphere. The magnetic storms that occurred on 7, 9, 12 and 15 March 2012 were different in nature. The largest change in the total electron content was observed during the storm of 9 March. This storm was associated with an interplanetary coronal mass ejection on 7 March that arrived on Earth 2 days later. The other analyzed events in 2013 and 2015 occurred on the same day of year-17 March. They were triggered by coronal mass ejections, which also hit the Earth magnetosphere at the same time of day. However, again the observed response of the ionosphere to these events was different.