EIR is an abbreviation of "Equipment Identity Register" node. There are two reference points (S13, S13') , which use EIR.
Interface between the MME and the EIR is known as S13. whereas interface between the SGSN and EIR is known as S13'.
EIR is used to authenticate ME (Mobile Equipment).
Two diameter messages "ME-Identity Check Request" and "ME-Identity Check Answer" are used as part of ME-Identity Check procedure. This procedure is being used to check the current status of UE equipment. Ex- suppose UE is blacklist since it was stolen.
When someone attach to the network using same stolen equipment. MME checks the equipment status from EIR. Depend on the response from EIR, MME takes subsequent actions for that UE.
In LTE procedure, as part of attach procedure, MME may sends "Identity Request" NAS message to get IMEI from UE. And receives "Identity Response" message from the UE. Once it receives the IMEI from the UE. MME may execute "ME-Identity Check Procedure" if MME is configured to do.