For every k, a 3-manifold with an involution has ordinary Dehn surgery number k and equivariant Dehn surgery number 2k.
Mallick,Knot Floer homology and surgery on equivariant knots, J
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Unbounded Gaps Between Ordinary and Equivariant Dehn Surgery Numbers
For every k, a 3-manifold with an involution has ordinary Dehn surgery number k and equivariant Dehn surgery number 2k.