Mezue ahịrịokwu na-esonụ: Vereitinov ruru eru maka ihe omume igwu mmiri abụọ na 2004 Summer Olympics na Athens, site na ikpochapụ FINA B-cut nke 1: 52.55 (200 m freestyle) site na
Asọmpi Iko Mba Europe na Madrid, Spain. Na 200 m freestyle, Vereitinov kpuchiri oge kachasị mma ya nke 1: 51.38 iji bute okpomọkụ nke atọ, mana ọ gwụchara naanị n'ọnọdụ iri abụọ na asaa site na mmalite nke ụtụtụ. Ya na Serhiy Fesenko, Serhiy Advena, na Maksym Kokosha jikọrọ aka na 4 × 200 m freestyle relay. Na-egwu mmiri nke atọ na okpomọkụ nke mbụ, Vereitinov dekọtara nkewa nke 1: 50.34, mana ndị Ukraine biri na nke isii na nke iri na abụọ n'ozuzu, na oge ikpeazụ nke 7: 24.13.