The geophysical and geological indications (pockmarks, gas chimneys, salt domes, etc.) that have been traced on the seabed using multi–beam echo–sounders and side–scan sonars, as well as the corresponding seismic surveys in the region South, South–west and South– east of Cyprus, as well as the corresponding international interest of investors, especially in the marine region of the Levantine Basin, lead to the conclusion that, from a geopolitical perspective, Greece must be urged to accelerate the consolidation of its sovereign rights and understand anew and in practical terms, that “Cyprus is not far away, not at all actually”. With respect to Kastellorizo and the submarine area of its EEZ, it is noted that de-tailed geophysical, bathymetric and sediment surveys have confirmed the fact that the region of the submarine Anaximander mountains presents active mud volcanoes, linked to the presence of gas hydrates. Samples of gas hydrates were collected using indicative samplings in mud volcanoes thoroughly mapped in sub–seabed layers of no more 1.5 m deep. Their form is “ice crystal”. New mud volcanoes were also discovered (“Athens” and “Thessaloniki”). Gas hydrates were found in samplings conducted on–board the M/V “Thessaloniki”. Based on preliminary assessments, the total capacity of the mud volcanoes of the Anaximander mountains complex is estimated between 2.56 6.40 c. km.1.