Interpolating between multi-center microstate geometries

We study interpolation between two multi-center microstate geometries in 4d/5d that represent Lunin-Mathur geometries with circular profiles. The interpolating solution is a Lunin-Mathur geometry with a helical profile, and is represented by a 2-center solution with a codimension-2 source. The interpolating 2-center solution exhibits interesting features such as some of the charges being delocalized, and some of the charges getting transferred from the codimension-2 center to the other, codimension-3 center as the interpolation proceeds. We also discuss the spectral flow of this entire process and speculate on the relevance of such solutions to understanding general microstates of 3-charge black holes.