data1 = {{{0, 2}, {1, 4}}, {{0, 2}, {1, 8}}};
data2 = {{{0, 3}, {3, 4}}, {{1, 5}}};
Manipulate[
   Show[
      ListLinePlot[data1[[n]], PlotRange -> {0, 10}, Joined -> true],
      ListLinePlot[data2[[n]], PlotRange -> {0, 10}, Joined -> true],
      {n, 1, 2, 1}]]

data1 = {{{0, 2}, {1, 4}}, {{0, 2}, {1, 8}}};
data2 = {{{0, 3}, {3, 4}}, {{1, 5}}};
    Show /@ Transpose @  (Table[
       ListLinePlot[#[[n]], PlotRange -> {0, 10}, Joined -> True], {n,
         1, 2, 1}] & /@ {data1, data2}) // ListAnimate

Manipulate[
 Show[ListLinePlot[data1[[n]], PlotRange -> {0, 10}, Joined -> true],
  ListLinePlot[data2[[n]], PlotRange -> {0, 10}, Joined -> true], {n,
   1, 2, 1}]]