(II) Presents in -αινω and -αιρω are formed from verb-stems in -αν and -αρ, the y being thrown back to unite with the vowel of the verb-stem ( cross111). Thus, φαίνω
a. Many verbs add -yω to the weak form of the stem, as ὀνομαίν-ω for ὀνομαν-yω from ὀνομ-yω, cp.
b. Hom. has κυ_δαίνω and κυ_δάνω
c. The ending αινω has been attached, by analogy, in θερμαίνω
Herbert Weir Smyth [n.d.], A Greek Grammar for Colleges; Machine readable text [info] [word count] [Smyth].