Let $(R,m)$ be a Cohen-Macaulay local ring, I and J are ideals of height $r.$ Then we say $I$ is directly linked to $J$, i.e. $I \sim J$ if there exists an ideal K generated by a regular sequence $x_1,\ldots,x_r$ such that $K\subset I\cap J,$ $I=K:J$ and $J=K:I.$
We say $I$ is linked to $J$ if there exist ideals $I_1,\ldots,I_s$ of height $r$ and generated by regular sequences such that $I\sim I_1, I_1\sim I_2,\ldots, I_s\sim J.$
Question: Is the operation "$I$ is linked to $J$" an equivalence relation? Particularly I do not understand how it is reflexive?
enter link description here [Linkage and the Koszul Homology of Ideals - C. Huneke]