Connection system between a trigger dispensing head and a bottle of a dispensing device, comprising: - a neck of the bottle having a circular cylindrical outer surface on which are found: A) a reference region (100,200,300) having a reference passage or a reference guide (202,302) for a snap-engagement; B) a first catch region (120,220,320) circumferentially flanking the reference region, provided with a first catch guide (122,222,322), having a first catch entry passage (122"', 222"', 322"'), and a first catch slide (126,226,326) having a first catch exit passage (126"',226"',326"'); C) a shelf region (140,240,340) circumferentially flanking the first catch region, provided with an upper shelf (142,242,342); D) a second catch region (160,260,360) circumferentially flanking the shelf region, provided with a second catch guide (162,262,362), having a second catch entry passage (162", 262′′′, 362'"), and a second catch slide (166, 266,366) having a second catch exit passage (166′′′,266′′′,366′′′); - a skirt of the dispensing head consisting of a skirt wall having a free skirt edge, comprising: a) a rigid reference tooth or a flexible reference tab (280, 380); b) a first flexible tab (184,284,384) and a first rigid tab tooth (188,288,388) located near the first tab between said first tab and the skirt edge; c) a second flexible tab (186,286,386) and a second rigid tab tooth (190,290,390), located near the second tab, between said second tab and the skirt edge; wherein - exclusively in one predetermined angular position between the neck and the skirt, wherein i) the reference tooth is aligned with the reference passage or the reference tab is aligned with the reference guide, the axial snap-engagement between the skirt and the neck is possible (aligned engagement configuration). - a neck of the bottle having a circular cylindrical outer surface on which are found: A) a reference region (100,200,300) having a reference passage or a reference guide (202,302) for a snap-engagement; B) a first catch region (120,220,320) circumferentially flanking the reference region, provided with a first catch guide (122,222,322), having a first catch entry passage (122"', 222"', 322"'), and a first catch slide (126,226,326) having a first catch exit passage (126"',226"',326"'); C) a shelf region (140,240,340) circumferentially flanking the first catch region, provided with an upper shelf (142,242,342); D) a second catch region (160,260,360) circumferentially flanking the shelf region, provided with a second catch guide (162,262,362), having a second catch entry passage (162", 262′′′, 362'"), and a second catch slide (166, 266,366) having a second catch exit passage (166′′′,266′′′,366′′′); A) a reference region (100,200,300) having a reference passage or a reference guide (202,302) for a snap-engagement; B) a first catch region (120,220,320) circumferentially flanking the reference region, provided with a first catch guide (122,222,322), having a first catch entry passage (122"', 222"', 322"'), and a first catch slide (126,226,326) having a first catch exit passage (126"',226"',326"'); C) a shelf region (140,240,340) circumferentially flanking the first catch region, provided with an upper shelf (142,242,342); D) a second catch region (160,260,360) circumferentially flanking the shelf region, provided with a second catch guide (162,262,362), having a second catch entry passage (162", 262′′′, 362'"), and a second catch slide (166, 266,366) having a second catch exit passage (166′′′,266′′′,366′′′); - a skirt of the dispensing head consisting of a skirt wall having a free skirt edge, comprising: a) a rigid reference tooth or a flexible reference tab (280, 380); b) a first flexible tab (184,284,384) and a first rigid tab tooth (188,288,388) located near the first tab between said first tab and the skirt edge; c) a second flexible tab (186,286,386) and a second rigid tab tooth (190,290,390), located near the second tab, between said second tab and the skirt edge; wherein a) a rigid reference tooth or a flexible reference tab (280, 380); b) a first flexible tab (184,284,384) and a first rigid tab tooth (188,288,388) located near the first tab between said first tab and the skirt edge; c) a second flexible tab (186,286,386) and a second rigid tab tooth (190,290,390), located near the second tab, between said second tab and the skirt edge; wherein - exclusively in one predetermined angular position between the neck and the skirt, wherein i) the reference tooth is aligned with the reference passage or the reference tab is aligned with the reference guide, the axial snap-engagement between the skirt and the neck is possible (aligned engagement configuration). i) the reference tooth is aligned with the reference passage or the reference tab is aligned with the reference guide, the axial snap-engagement between the skirt and the neck is possible (aligned engagement configuration).