  For immersed surfaces in the four-space, we have a generating set of the
Swenton--Hughes--Kim--Miller spatial moves that relate singular banded diagrams
of ambient isotopic immersions of those surfaces. We also have
Yoshikawa--Kamada--Kawauchi--Kim--Lee planar moves that relate marked graph
diagrams of ambient isotopic immersions of those surfaces. One can ask if the
former moves form a minimal set and if the latter moves form a generating set.
In this paper, we derive a minimal generating set of spatial moves for diagrams
of surfaces immersed in the four-space, which translates into a generating set
of planar moves. We also show that the complements of two equivalent immersed
surfaces can be transformed one another by a Kirby calculus not requiring the
1-1-handle or 2-1-handle slides. We also discuss the fundamental group of the
immersed surface-link complement in the four-space and a quandle coloring
invariant of an oriented immersed surface-link.
