Put in a/an or the: May Day which is not

The May Day which is not a bank holiday, is a celebration of the coming of spring. День мая, который не является праздничком банка, является празднование прихода весны.

A / an is indefinite article. The is definite article. Indefinite article is used with singular nouns. The meaning of indefinite article is one. A is used before consonant (a door) and an is used before vowel (an apple).

Definite article is used with noun which is already known.