  We investigate multifractal regularity for infinite conformal iterated
function systems (cIFS). That is we determine to what extent the multifractal
spectrum depends continuously on the cIFS and its thermodynamic potential. For
this we introduce the notion of regular convergence for families of cIFS not
necessarily sharing the same index set, which guarantees the convergence of the
multifractal spectra on the interior of their domain. In particular, we obtain
an Exhausting Principle for infinite cIFS allowing us to carry over results for
finite to infinite systems, and in this way to establish a multifractal
analysis without the usual regularity conditions. Finally, we discuss the
connections to the $\lambda$-topology introduced by Roy and Urbas{\'n}ki.
