It is known that, through hodograph (reciprocal) transformation, Degasperis-Procesi (DP) equation is linked to the negative flow of the Kaup-Kuperschmidt (KK) hierarchy while the Novikov equation is connected to the negative flow of the Sawada-Kotera (SK) hierarchy.  In this talk, we will show how to derive the DP and Novikov equations from the pseudo-3 reduction of a CKP hierarchy and how to derive their short limits from the 3-reduction of the same CKP hierarchy. We will also clarify a fact that a modified short pulse equation is connected to the short wave limits of the DP and Novikov equations via Miura transformations. In the last, we will explore the possible integrable equation which might have Miura links with the DP and Novikov equations.