I was reading a paper for recognizing interval graphs. Here is an excerpt from the paper:
Each interval graph has a corresponding interval model in which two intervals overlap if and only if their corresponding vertices are adjacent. Such a representation is usually far from unique. To eliminate uninteresting variations of the endpoint orderings, we shall consider the following block structure of endpoints: Denote the right (resp. left) endpoint of an interval $u$ by $R(u)$ (resp. $L(u)$). In an interval model, define a maximal contiguous set of right (resp. left) endpoints as an R-block (resp. L-block). Thus, the endpoints can be grouped as a left-right block sequence. Since an endpoint block is a set, the endpoint orderings within a block are ignored. It is easy to see that the overlapping relationship does not change if one permute the endpoint order within each block. Define two interval models for $G$ to be equivalent if either their left-right block sequences are identical or one is the reversal of the other.
I am unable to understand the notion of equivalent intervals. Can someone help me?