Is it possible to have annealing without creep? Annealing can repair a material by allowing atoms to find the minimum energy state; since solids have a surface tension this process will allow cracks to fuse and reverse fatigue. However, annealing comes with it's evil twin: creep. If the atoms have enough thermal energy to remove defects form the crystal they likely will also slowly move in the direction of applied force; the material behaves like a very viscous liquid.
But is it possible, given the right material and temperature, to have annealing without creep? If the energy barrier to remove a dislocation is less than the energy barrier to pull an atom out of the crystal lattice, there could be a temperature sweet-spot in which materials wouldn't fatigue but wouldn't creep either?
 A: In metals creep proceeds by dislocation movement, and this is also what happens in annealing. Therefore annealing is inseparable from creep because they both occur by the same mechanism.
A: Your question mentions 'fusing' cracks.  I think you may be asking whether there are actual examples of what is sometimes referred to as "reversible crack growth."  This is often the ideal case discussed when students are learning crack mechanics theory.  The closest approximation to reversible crack growth demonstrated in the laboratory that I am aware of are experiments performed using cleavage cracks in mica. The cracks must be made under a vacuum to avoid contamination of the surfaces.  When the applied stress is removed the crack can 'heal.'  It's never perfectly reversible, because of reasons that can include surface contamination and plastic deformation near the crack tip.
Another strain mechanism that might be approximated (under simple conditions) is possibly stress induced twinning. If the applied stresses are removed and the twinned crystal is heated, the twins might reverse. 
'Removing' a dislocation from a crystal lattice means moving the dislocation to a point where it is 'annihilated' by reaction with other defects or a surface.  A dislocation may move to a free surface, and out of the lattice. A dislocation loop may shrink down to no radius. Two dislocation segments of exactly opposite Burgers vector may move towards each other cancel out. Dislocation motion means plastic strain. It would be rare that all the strains would cancel out exactly, so in most real cases annealing probably result in at least a little residual strain.
