  In this paper we have investigated enumeration orders of elements of r.e.
sets enumerated by means of Turing machines. We have defined a reducibility
based on enumeration orders named "Enumeration Order Reducibility" on
computable functions and also r.e. sets and studied their properties. Based on
this reducibility we introduce an equivalence relation "Enumeration Order
Equivalency". We have reached some properties of it. In subsequent, we have
introduced another concept named "type-2 Enumeration Order Equivalency" and
studied its properties too.
