For s=1 TM:

In[]:=
NeighboringConfigurations[{pos_Integer,tape_List},k_Integer:2]:=Catenate[Table[{pos1,tape1},{pos1,Max[1,pos-1],Min[Length[tape],pos+1]},{tape1,Table[ReplacePart[tape,posi],{i,0,k-1}]}]]
In[]:=
Tuples[{0,1},3]
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{{0,0,0},{0,0,1},{0,1,0},{0,1,1},{1,0,0},{1,0,1},{1,1,0},{1,1,1}}
In[]:=
With[{len=3},Graph[Flatten[Table[{pos,tape}#&/@NeighboringConfigurations[{pos,tape},2],{pos,3},{tape,Tuples[{0,1},len]}],2],VertexShapeFunction(Inset[RulePlot[TuringMachine[2506(*needsasampleofruletype*)],{{1,#2[[1]]},#2[[2]]},0,MeshAll,FrameFalse,ImageSize40],#1]&)]]
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In[]:=
With[{len=1},Graph[Flatten[Table[{pos,tape}#&/@NeighboringConfigurations[{pos,tape},2],{pos,3},{tape,Tuples[{0,1},len]}],2],VertexShapeFunction(Inset[RulePlot[TuringMachine[2506(*needsasampleofruletype*)],{{1,#2[[1]]},#2[[2]]},0,MeshAll,FrameFalse,ImageSize40],#1]&)]]
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With[{len=2},Graph[Flatten[Table[{pos,tape}#&/@NeighboringConfigurations[{pos,tape},2],{pos,3},{tape,Tuples[{0,1},len]}],2],VertexShapeFunction(Inset[RulePlot[TuringMachine[2506(*needsasampleofruletype*)],{{1,#2[[1]]},#2[[2]]},0,MeshAll,FrameFalse,ImageSize40],#1]&)]]
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With[{g=With[{t=2},MultiwayTuringMachine[AllDeltaTMRules[{1,2}],{{1,t+1,0},Table[0,2t+1]},t,"StatesGraph","IncludeEventInstances"False,PerformanceGoal"Quality",VertexSize.8{1,1/(2t+1)}]]},Subgraph[g,Select[VertexList[g],Abs[ToExpression[#][[1,3]]]<2&]]]
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In[]:=
With[{g=With[{t=3},MultiwayTuringMachine[AllDeltaTMRules[{1,2}],{{1,t+1,0},Table[0,2t+1]},t,"StatesGraph","IncludeEventInstances"False,PerformanceGoal"Quality",VertexSize.8{1,1/(2t+1)}]]},Subgraph[g,Select[VertexList[g],Abs[ToExpression[#][[1,3]]]<3&]]]
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In[]:=
With[{g=With[{t=3},MultiwayTuringMachine[AllDeltaTMRules[{1,2}],{{1,t+2,0},Table[0,2t+3]},t,"StatesGraph","IncludeEventInstances"False,PerformanceGoal"Quality",VertexSize.8{1,1/(2t+1)}]]},Subgraph[g,Select[VertexList[g],Abs[ToExpression[#][[1,3]]]<3&]]]
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