Inequivalent handlebody-knots with homeomorphic complements

We distinguish the handlebody-knots 5 ₁, 6 ₄ and 5 ₂, 6 ₁₃ in the table, due to Ishii et al, of irreducible handlebody-knots up to six crossings. Furthermore, we construct two infinite families of handlebody-knots, each containing one of the pairs 5 ₁, 6 ₄ and 5 ₂, 6 ₁₃, and show that any two handlebody-knots in each family have homeomorphic complements but they are not equivalent.