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Here's a direct list-manipulation approach using a variation of Heike's answeranswer for combining subsets with similar terms:

Cases[list1, {___, Alternatives @@ #, ___}, 2] & /@ list2 //. 
    x_ :> Union @@@ Gather[x, Intersection@## =!= {} &]

(* {{{1, 2}, {31, 32}, {45, 46}}, {{5, 6}, {27, 28}}, {{7, 8}, {41, 42}}, 
    {{21, 22}, {25, 26}, {29, 30}}, {{33, 34}, {35, 36}, {37, 38}}, {{47, 48}, {49, 50}}} *)

Here's a direct list-manipulation approach using a variation of Heike's answer for combining subsets with similar terms:

Cases[list1, {___, Alternatives @@ #, ___}, 2] & /@ list2 //. 
    x_ :> Union @@@ Gather[x, Intersection@## =!= {} &]

(* {{{1, 2}, {31, 32}, {45, 46}}, {{5, 6}, {27, 28}}, {{7, 8}, {41, 42}}, 
    {{21, 22}, {25, 26}, {29, 30}}, {{33, 34}, {35, 36}, {37, 38}}, {{47, 48}, {49, 50}}} *)

Here's a direct list-manipulation approach using a variation of Heike's answer for combining subsets with similar terms:

Cases[list1, {___, Alternatives @@ #, ___}, 2] & /@ list2 //. 
    x_ :> Union @@@ Gather[x, Intersection@## =!= {} &]

(* {{{1, 2}, {31, 32}, {45, 46}}, {{5, 6}, {27, 28}}, {{7, 8}, {41, 42}}, 
    {{21, 22}, {25, 26}, {29, 30}}, {{33, 34}, {35, 36}, {37, 38}}, {{47, 48}, {49, 50}}} *)
1
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Here's a direct list-manipulation approach using a variation of Heike's answer for combining subsets with similar terms:

Cases[list1, {___, Alternatives @@ #, ___}, 2] & /@ list2 //. 
    x_ :> Union @@@ Gather[x, Intersection@## =!= {} &]

(* {{{1, 2}, {31, 32}, {45, 46}}, {{5, 6}, {27, 28}}, {{7, 8}, {41, 42}}, 
    {{21, 22}, {25, 26}, {29, 30}}, {{33, 34}, {35, 36}, {37, 38}}, {{47, 48}, {49, 50}}} *)