  Whether live cell membranes show miscibility phase transitions (MPTs), and if
so, how they fluctuate near the transitions remain outstanding unresolved
issues in physics and biology alike.
  Motivated by these questions we construct a generic hydrodynamic theory for
lipid membranes {{that are active, due for instance, to the molecular motors in
the surrounding cytoskeleton, or active protein components in the membrane
itself}}. We use this to uncover a direct correspondence between membrane
fluctuations and MPTs. Several testable predictions are made: (i) generic {\em
active stiffening} with orientational long range order (flat membrane) or {\em
softening} with crumpling of the membrane, controlled by the {\em active
tension} and (ii) for mixed lipid membranes, capturing the nature of putative
MPTs by measuring the membrane conformation fluctuations. Possibilities of both
first and second order MPTs in mixed active membranes are argued for. Near
second order MPTs, active stiffening (softening) manifests as a {\em
super-stiff (super-soft) membrane}. Our predictions are testable in a variety
of {\em in-vitro} systems, e.g., live cytoskeletal extracts deposited on
liposomes and lipid membranes containing active proteins embedded in a passive
fluid.
