I think its DRAGONFLY:A dragonfly is an insect belonging to the order Odonata, the suborder Epiprocta or, in the strict sense, the infraorder Anisoptera. It is characterized by large multifaceted eyes, two pairs of strong transparent wings, and an elongated body.
if its DAMSELFLY, then: The Damselfly (Suborder Zygoptera) is an insect in the Order Odonata. Damselflies are similar to dragonflies, but the adults can be differentiated by the fact that the wings of most damselflies are held along the body when at rest. Furthermore, the hindwing of the damselfly is essentially similar to the forewing, while the hindwing of the dragonfly broadens near the base, caudal to the connecting point at the body. Damselflies are also usually smaller, weaker fliers than dragonflies, and their eyes are separated.
MAYFLY: Mayflies are insects which belong to the Order Ephemeroptera (from the Greek ephemeros = "short-lived", pteron = "wing", referring to the short life span of adults). They have been placed into an ancient group of insects termed the Paleoptera, which also contains the dragonflies and damselflies. They are aquatic insects whose immature stage (called naiad or, colloquially, nymph) usually lasts one year in fresh water. The adults are short-lived, from a few hours to a few days depending on the species. About 2,500 species are known worldwide, including about 630 species in North America. Common names for mayflies include "dayfly", "shadfly", "Canadian soldier", and "fishfly".