Your functions list[B,n] are the result of a sorting eigenvalues in increasing order:

list[B_?NumericQ] := Sort@Eigenvalues[H[N[B]]]

I don't expect them to cross.

Perhaps there is a misunderstanding about what we mean by "curve". The functions list[B, n] that you plot are continuous, but their graphics go zigzag.

In the circle I see a violet "curve" on top, below it a yellow curve, then a green one, then a dark red one, and finally a blue curve. They touch each other, but they do not cross.

I think that the zigzag is to be expected. Try a simpler example:

mat[x_?NumericQ] := {{2 x, 0}, {0, x + 1}};
eigen1[x_?NumericQ] := Min[Eigenvalues[mat[x]]];
eigen2[x_?NumericQ] := Max[Eigenvalues[mat[x]]];
Plot[{eigen1[x], eigen2[x]}, {x, 0, 2}]

The curves of eigen1 and eigen2 go zigzag and they do not cross.

OK. Could you please elaborate your answer further? I am unable to follow , "how can I draw the curves to follow the crossings?" Have you any idea how can I remove the zigzag trend among the curves?

You are right but in my case zigzag trend should not be there. Any way to systematically get rid of this trend?

Crossposted here.